PHILLIPS, Circuit Judge.
The city of Fort Collins, Colorado, enacted a public-nudity ordinance that imposes no restrictions on male toplessness but prohibits women from baring their *795breasts below the areola. See Fort Collins, Colo., Mun. Code § 17-142 (2015). In response, Free the Nipple, an unincorporated association, and two individuals, Brittiany Hoagland and Samantha Six (collectively, "the Plaintiffs"), sued the City in federal district court. They alleged (among other things) that the ordinance violated the Equal Protection Clause, U.S. Const. amend. XIV, § 1, and they asked for a preliminary injunction to halt enforcement of the ordinance. The district court agreed. It enjoined the City, pending the resolution of the case's merits, from implementing the ordinance "to the extent that it prohibits women, but not men, from knowingly exposing their breasts in public." Free the Nipple-Fort Collins v. City of Fort Collins , 237 F.Supp.3d 1126, 1135 (D. Colo. 2017). The City then brought this interlocutory appeal to challenge the injunction.
The appeal presents a narrow question: Did the district court reversibly err in issuing the preliminary injunction? We answer no. Exercising interlocutory jurisdiction under 28 U.S.C. § 1292(a)(1), we affirm the district court's judgment and remand the case to that court for further proceedings consistent with this opinion.
BACKGROUND
In 2015, after substantial public debate, the Fort Collins city council enacted this public-nudity ordinance:
No female who is ten (10) years of age or older shall knowingly appear in any public place with her breast exposed below the top of the areola and nipple while located: (1) In a public right-of-way, in a natural area, recreation area or trail, or recreation center, in a public building, in a public square, or while located in any other public place; or (2) On private property if the person is in a place that can be viewed from the ground level by another who is located on public property and who does not take extraordinary steps, such as climbing a ladder or peering over a screening fence, in order to achieve a point of vantage. .... The prohibition [on female toplessness] does not extend to women breastfeeding in places they are legally entitled to be.
Fort Collins, Colo., Mun. Code § 17-142(b), (d). Any person who violates this ordinance "shall be guilty of a misdemeanor" and "shall be punished" by a fine of up to $2,650, or up to 180 days in jail, or both. Id. § 1-15(a).
The Plaintiffs immediately sued the City in federal district court, alleging that the public-nudity ordinance violates the Free Speech Clause of the First Amendment and the Equal Protection Clause of the Fourteenth Amendment to the U.S. Constitution, as well as the Equal Rights Amendment to the Colorado Constitution. Their complaint includes a jury-trial demand and a prayer for relief asking the court (1) to declare the ordinance "unconstitutional on its face and as applied to [the] Plaintiffs" and (2) to prevent the ordinance's enforcement. Appellant's App. vol. 1 at 20. Separately, the Plaintiffs moved for a preliminary injunction blocking enforcement of the ordinance and "prohibit[ing] [the City] from discriminatorily arresting [the] Plaintiffs, and all others similarly situated, when they engage in the protected activity of standing topless in public places in Fort Collins, Colorado." Id. at 22.
The City countered with a motion to dismiss arguing that the Plaintiffs had failed to state any claim on which relief could be granted, see Fed. R. Civ. P. 12(b)(6), and a response to the Plaintiffs' preliminary-injunction motion. In the latter, the City asserted that a preliminary injunction would unfairly burden the public *796"by exposure to public nudity" and urged the court to deny the motion. Appellant's App. vol. 2 at 33.
The district court first addressed the City's motion to dismiss. It granted the motion on the Plaintiffs' free-speech claim, agreeing with the City that "topless protests" aren't protected speech, but allowed the Plaintiffs' (federal) Equal Protection Clause and (state) Equal Rights Amendment claims to proceed. Free the Nipple-Fort Collins v. City of Fort Collins , 216 F.Supp.3d 1258, 1262 (D. Colo. 2016). Next, the court turned to the Plaintiffs' preliminary-injunction motion. After holding a hearing on the matter, it granted the motion, ruling that the ordinance likely violated the Equal Protection Clause,1 and issued the requested injunction. Free the Nipple , 237 F.Supp.3d at 1128. Pending trial (or other resolution of the case), the preliminary injunction blocks the City from enforcing its public-nudity ordinance "to the extent that it prohibits women, but not men, from knowingly exposing their breasts in public." Id. at 1135.
The City then brought this interlocutory appeal defending the constitutionality of its public-nudity ordinance and challenging the preliminary injunction.
DISCUSSION
In its appeal, the City asks us to vacate the district court's preliminary injunction so that it can fully enforce its public-nudity ordinance.2 The City argues that the ordinance's unequal treatment of male and female toplessness survives constitutional scrutiny, making it likely that the Plaintiffs will lose a merits trial and, in the meantime, precluding them from getting injunctive relief. Before we address the City's argument, we define our standard of review and explain the rules governing the grant (or denial) of a preliminary injunction. We'll then apply that framework to determine whether the district court reversibly erred when it issued the preliminary injunction.
I. Standard of Review
District courts have discretion over whether to grant preliminary injunctions, United States ex rel. Citizen Band Potawatomi Indian Tribe v. Enter. Mgmt. Consultants, Inc. , 883 F.2d 886, 889 (10th Cir. 1989), and we will disturb their decisions only if they abuse that discretion, Fish v. Kobach , 840 F.3d 710, 723 (10th Cir. 2016). A district court's decision crosses the abuse-of-discretion line if it rests on an erroneous legal conclusion or lacks a rational basis in the record. Id. (quoting Awad v. Ziriax , 670 F.3d 1111, 1125 (10th Cir. 2012) ). As we review a district court's decision to grant or deny a preliminary injunction, we thus examine the court's *797factual findings for clear error and its legal conclusions de novo. Id.
II. The Legal Standards Governing Preliminary Injunctions
"A preliminary injunction is an extraordinary remedy, the exception rather than the rule." Enter. Mgmt. Consultants, Inc. , 883 F.2d at 888. To succeed on a typical preliminary-injunction motion, the moving party needs to prove four things: (1) that she's "substantially likely to succeed on the merits," (2) that she'll "suffer irreparable injury" if the court denies the injunction, (3) that her "threatened injury" (without the injunction) outweighs the opposing party's under the injunction, and (4) that the injunction isn't "adverse to the public interest." Beltronics USA, Inc. v. Midwest Inventory Distrib., LLC , 562 F.3d 1067, 1070 (10th Cir. 2009).
But courts "disfavor" some preliminary injunctions and so require more of the parties who request them. See Schrier v. Univ. of Colo. , 427 F.3d 1253, 1258-59 (10th Cir. 2005). Disfavored preliminary injunctions don't merely preserve the parties' relative positions pending trial. Id. Instead, a disfavored injunction may exhibit any of three characteristics: (1) it mandates action (rather than prohibiting it), (2) it changes the status quo, or (3) it grants all the relief that the moving party could expect from a trial win. Awad , 670 F.3d at 1125 (citing Summum v. Pleasant Grove City , 483 F.3d 1044, 1048-49 (10th Cir. 2007) ); see also Phillip v. Fairfield Univ. , 118 F.3d 131, 133 (2d Cir. 1997) (explaining that an injunction is "mandatory" if "its terms would alter, rather than preserve, the status quo by commanding some positive act"). To get a disfavored injunction, the moving party faces a heavier burden on the likelihood-of-success-on-the-merits and the balance-of-harms factors: She must make a "strong showing" that these tilt in her favor. Fish , 840 F.3d at 724 (quoting Beltronics , 562 F.3d at 1071 ).
On appeal, the City invokes an even higher standard that requires movants who, like the Plaintiffs, seek to disturb the status quo to "demonstrate not only that the four requirements for a preliminary injunction are met but also that they weigh heavily and compellingly in [the movants'] favor." Appellant's Opening Br. at 8 (quoting Kikumura v. Hurley , 242 F.3d 950, 955 (10th Cir. 2001) ). But we "jettison[ed]" the heavily-and-compellingly requirement over a decade ago. O Centro Espirita Beneficiente Uniao do Vegetal v. Ashcroft , 389 F.3d 973, 975 (10th Cir. 2004) (per curiam), aff'd sub nom Gonzales v. O Centro Espirita Beneficiente Uniao do Vegetal , 546 U.S. 418, 126 S.Ct. 1211, 163 L.Ed.2d 1017 (2006). Today, "the requirement that a movant requesting a disfavored injunction must make a showing that the traditional four factors weigh heavily and compellingly in [the movant's] favor is no longer the law of the circuit." Schrier , 427 F.3d at 1261.
The preliminary injunction at issue here prevents the City from fully enforcing its public-nudity ordinance. In so doing, the district court concluded that the injunction both "alters the status quo and affords the movants all the relief they could recover at the conclusion of a full trial on the merits." Free the Nipple , 237 F.Supp.3d at 1130. This conclusion led the district court to apply the heightened disfavored-injunction standard and to require strong showings from the Plaintiffs on the first and third factors. Id. And though we have doubts that the heightened standard applies here, we need not decide which standard to apply-the plaintiffs prevail under the *798heightened standard and, therefore, under both.3
III. Application
On appeal, the City disputes that the Plaintiffs can prevail on any of the four preliminary-injunction factors, but its argument hinges on the first factor: the likelihood that the Plaintiffs will succeed on the merits. According to the City, all four preliminary-injunction factors favor the City because the Plaintiffs lack a viable equal-protection claim and will likely lose on the merits. The fate of this preliminary injunction thus turns largely, if not entirely, on the strength of the Plaintiffs' equal-protection claim. But the City challenges each preliminary-injunction factor, so we address each (though we focus on the first).
A. The First Factor: Likelihood of Success on the Merits
The heightened standard applicable to disfavored preliminary injunctions requires the Plaintiffs to make a strong showing that their equal-protection claim is substantially likely to succeed on its merits. Fish , 840 F.3d at 723-24. The City contests the district court's conclusion that the Plaintiffs made this showing. That conclusion, according to the City, reflects "a fundamental misunderstanding" of Supreme Court precedent and "a misapprehension of the purpose and effect" of the public-nudity ordinance. Appellant's Opening Br. at 9.
We begin our analysis with an outline of the relevant equal-protection principles. Applying those principles, we then assess the merits of the Plaintiffs' equal-protection claim to determine whether the district court abused its discretion when it concluded that the likelihood-of-success factor tilts toward the Plaintiffs.
1. The Equal Protection Clause and Gender-Based Classifications
"No State shall ... deny to any person within its jurisdiction the equal protection of the laws." U.S. Const. amend. XIV, § 1. The Equal Protection Clause, as the U.S. Supreme Court has interpreted it, directs "that all persons similarly situated should be treated alike." City of Cleburne v. Cleburne Living Ctr. , 473 U.S. 432, 439, 105 S.Ct. 3249, 87 L.Ed.2d 313 (1985). "At a minimum," it requires that any statutory classification be "rationally related to a legitimate governmental purpose."
*799Clark v. Jeter , 486 U.S. 456, 461, 108 S.Ct. 1910, 100 L.Ed.2d 465 (1988). But more stringent judicial scrutiny attaches to classifications based on certain "suspect" characteristics. See City of Cleburne , 473 U.S. at 440, 105 S.Ct. 3249. These (often immutable) characteristics seldom provide a "sensible ground for differential treatment." Id.
Gender, for instance, "frequently bears no relation to ability to perform or contribute to society," and statutes that differentiate between men and women "very likely reflect outmoded notions" about their "relative capabilities." Id. at 440-41, 105 S.Ct. 3249 (quoting Frontiero v. Richardson , 411 U.S. 677, 686, 93 S.Ct. 1764, 36 L.Ed.2d 583 (1973) ). As a result, gender-based classifications "call for a heightened standard of review," id. at 440, 105 S.Ct. 3249, a standard dubbed "intermediate scrutiny" because it lies "[b]etween the[ ] extremes of rational basis review and strict scrutiny." Clark , 486 U.S. at 461, 108 S.Ct. 1910. To survive intermediate scrutiny, a gender-based classification needs "an exceedingly persuasive justification." J.E.B. v. Alabama ex rel. T.B. , 511 U.S. 127, 136, 114 S.Ct. 1419, 128 L.Ed.2d 89 (1994). The classification must serve "important governmental objectives" through means "substantially related to" achieving those objectives. United States v. Virginia , 518 U.S. 515, 533, 116 S.Ct. 2264, 135 L.Ed.2d 735 (1996) (quoting Miss. Univ. for Women v. Hogan , 458 U.S. 718, 724, 102 S.Ct. 3331, 73 L.Ed.2d 1090 (1982) ); see also Craig v. Boren , 429 U.S. 190, 197-99, 97 S.Ct. 451, 50 L.Ed.2d 397 (1976) (defining, for the first time, this level of means-ends scrutiny).
The City acknowledges that a female-only topless ban is a gender-based classification and that, to pass muster under the Equal Protection Clause, gender-based classifications must satisfy intermediate scrutiny. But instead of drawing the logical conclusion-that female-only topless bans warrant intermediate scrutiny-the City interrupts the syllogism. It asserts that "[t]he fundamental requirement of any cognizable gender discrimination claim is invidious discrimination , not simply classification on the basis of gender." Appellant's Opening Br. at 10 (bolding removed).
Some of the Court's early equal-protection cases, such as 1979's Parham v. Hughes , did treat invidiousness as a "threshold" inquiry. 441 U.S. 347, 351, 99 S.Ct. 1742, 60 L.Ed.2d 269 (1979). Yet Parham , if never overruled, is outdated in light of the Court's more modern equal-protection jurisprudence.4 Since then, the Court has "consistently" recognized that statutes supposedly based on "reasonable considerations" may in fact reflect "archaic and overbroad generalizations about gender" or "outdated misconceptions concerning the role of females in the home rather *800than in the marketplace and world of ideas." J.E.B. , 511 U.S. at 135, 114 S.Ct. 1419 (quoting Schlesinger v. Ballard , 419 U.S. 498, 506-07, 95 S.Ct. 572, 42 L.Ed.2d 610 (1975), and Craig , 429 U.S. at 198-99, 97 S.Ct. 451 ). Today, heightened scrutiny "attends 'all gender-based classifications.' " Morales-Santana , 137 S.Ct. at 1689 (quoting J.E.B. , 511 U.S. at 136, 114 S.Ct. 1419 ).
Invidiousness still matters, but only in challenges to facially gender-neutral statutes that disproportionately and adversely impact one gender. See Personnel Adm'r v. Feeney , 442 U.S. 256, 259, 273-74, 99 S.Ct. 2282, 60 L.Ed.2d 870 (1979) (challenging Massachusetts's hiring preference for veterans, which worked "overwhelmingly to the advantage of males"). Here, however, the City has enacted, and the Plaintiffs have challenged, a public-nudity ordinance that prescribes one rule for women, requiring them to cover their breasts below the areola, and a different rule for men, allowing them to go topless as they please. Fort Collins, Colo., Mun. Code § 17-142(b). The ordinance creates a gender classification on its face, taking invidiousness out of the equation. The success of the Plaintiffs' equal-protection claim depends only on whether the ordinance survives intermediate scrutiny.
We turn to that question next, as we address the City's attack on the merits of the Plaintiffs' equal-protection claim and defense of its public-nudity ordinance.
2. The Merits of the Plaintiffs' Equal-Protection Claim
The district court characterized as "little more than speculation" the City's claim that banning only female toplessness furthered important governmental objectives. Free the Nipple , 237 F.Supp.3d at 1131. Instead, the court found:
The ordinance discriminates against women based on the generalized notion that, regardless of a woman's intent, the exposure of her breasts in public (or even in her private home if viewable by the public) is necessarily a sexualized act. Thus, it perpetuates a stereotype engrained in our society that female breasts are primarily objects of sexual desire whereas male breasts are not.
Id. at 1132. As a result, the court concluded, the Plaintiffs demonstrated "a strong likelihood that they will succeed at the permanent injunction trial in establishing that [the City's public-nudity ordinance] violates the Equal Protection Clause." Id. at 1133.
The City challenges this conclusion on appeal. It argues that, "in light of the differences between male and female breasts," prohibiting only female toplessness is substantially related to an important governmental objective, as a sizeable majority of other courts have found. Appellant's Opening Br. at 19. We address the City's argument in two parts. First, we discuss the focus of the City's defense-the physical differences between male and female breasts-and explain how such differences affect the constitutional analysis. Second, we determine whether the City's female-only toplessness ban survives constitutional scrutiny.
a. Physical Differences
In defending the constitutionality of its public-nudity ordinance, the City emphasizes the physical, social, and sexual characteristics particular to the female breast. Citing a Wikipedia article (which is titled "Breast" but discusses only the female version) the City argues that women's breasts "have social and sexual characteristics," although their "primary function" is breastfeeding infants. Appellant's Opening Br. at 12; see Breast , Wikipedia: The Free Encyclopedia, https://en.wikipedia.org/wiki/Breast (last visited Apr. 18, 2018). The *801article, as quoted by the City, describes female breasts ("and especially the nipples") as "among the various human erogenous zones" and claims that "it is common to press or massage them with hands or orally before or during sexual activity." Appellant's Opening Br. at 12. Breasts, the City claims, "can figure prominently in a woman's perception of her body image and sexual attractiveness" and "have a hallowed sexual status" in Western culture, "arguably more fetishized than either sex's genitalia." Id. But "the sexualization of women's breasts," according to the City, "is not solely a product of societal norms, but of biology." Id. at 13. Research suggests that women's breasts have greater "tactile sensitivity" than men's. Id. at 13-14 (citing J.E. Robinson & R.V. Short, Changes in Breast Sensitivity at Puberty, During the Menstrual Cycle, and at Parturition , British Medical Journal 1, 1188-91 (1977) ).5
Though we're wary of Wikipedia's user-generated content, we agree with the district court that "[o]f course" inherent physical differences exist between women's and men's breasts-most obviously, the unique potential to nourish children. Free the Nipple , 237 F.Supp.3d at 1132 ; see also Crispin v. Christian Audigier, Inc. , 717 F.Supp.2d 965, 976 n.19 (C.D. Cal. 2010) (discussing the dangers of relying on Wikipedia); R. Jason Richards, Courting Wikipedia , 44 Trial 62 (Apr. 2008) ("Since when did a Web site that any Internet surfer can edit become an authoritative source by which ... lawyers could craft legal arguments[ ] and judges could issue precedents?"). But that doesn't resolve the constitutional question.
"Physical differences between men and women," the Court has recognized, "are enduring." Virginia , 518 U.S. at 533, 116 S.Ct. 2264. And in some cases, the Court has found, such differences justify differential treatment. See, e.g. , Nguyen v. INS , 533 U.S. 53, 58-59, 68, 121 S.Ct. 2053, 150 L.Ed.2d 115 (2001) (upholding a paternal-acknowledgment requirement in a citizenship statute that treated unwed mothers differently than unwed fathers, in part because the statute addressed "an undeniable difference" between women and men: "at the moment of birth ... the mother's knowledge of the child and the fact of parenthood have been established in a way not guaranteed in the case of the unwed father"). But not always.
Any law premised on "generalizations about 'the way women are' "-or the way men are-will fail constitutional scrutiny because it serves no important governmental objective. Virginia , 518 U.S. at 550, 116 S.Ct. 2264 ; see also Morales-Santana , 137 S.Ct. at 1692 (rejecting, as one such generalization, "the obsolescing view that 'unwed fathers [are] invariably less qualified and entitled than mothers' to take responsibility for nonmarital children"). Generalizations, the Court has explained, "have a constraining impact, descriptive though they may be of the way many people still order their lives." Morales-Santana , 137 S.Ct. at 1692-93. They "may 'creat[e] a self-fulfilling cycle of discrimination that force[s] women to continue to assume the role of primary family caregiver.' " Id. at 1693 (alteration in original) (quoting Nev. Dep't of Human Res. v. Hibbs , 538 U.S. 721, 736, 123 S.Ct. 1972, 155 L.Ed.2d 953 (2003) ).
*802So, as we inquire into a gender-based classification's objectives, we must beware of stereotypes and their potential to perpetuate inequality. "Even if stereotypes frozen into legislation have 'statistical support,' " we must "reject measures that classify unnecessarily and overbroadly by gender when more accurate and impartial lines can be drawn." Morales-Santana , 137 S.Ct. at 1693 n.13 (citing J.E.B. , 511 U.S. at 139 n.11, 114 S.Ct. 1419 ); see also Cary Franklin, The Anti-Stereotyping Principle in Constitutional Sex Discrimination Law , 85 N.Y.U. L. Rev. 83, 138 n.296 (2010) ("The anti-stereotyping principle pervades both stages of [intermediate scrutiny], shaping what constitutes an important interest and what means qualify as sufficiently narrowly tailored to serve this interest.").
With those principles in mind, we now apply the intermediate-scrutiny doctrine to the City's female-only toplessness ban.
b. Intermediate Scrutiny
To determine whether the City's public-nudity ordinance survives intermediate scrutiny, we first identify the City's proffered reasons for enacting a gender-based classification. Then, we ask whether the City's reasons qualify as important governmental objectives and, if so, whether the gender-based means employed substantially serve those objectives. See Morales-Santana , 137 S.Ct. at 1690 (citing Virginia , 518 U.S. at 533, 116 S.Ct. 2264 ).
The City argues that the inherently sexual nature of the female breast, as opposed to the male breast, raises "myriad concerns" with "permitting adult females to go topless in public without restriction." Appellant's Opening Br. at 18. The City refers us to the preliminary-injunction hearing, where three city officials-the deputy city manager, the assistant chief of police, and the city aquatics supervisor-described some of these concerns. The officials testified that female toplessness could disrupt public order, lead to distracted driving, and endanger children. Citing these concerns, the City claims that prohibiting only female toplessness serves to protect children from public nudity, to maintain public order, and to promote traffic safety.6 We address each rationale in turn.
i. Protecting Children from Public Nudity7
The capacity to breastfeed is the first attribute that, the City claims, sets the female breast apart. Yet the City's public-nudity ordinance expressly exempts breastfeeding women from the female-toplessness ban, so even children who weren't exposed to their mothers' breasts as breastfeeding infants may still see a naked female breast if they pass a woman breastfeeding in public-her right under state law. Fort Collins, Colo., Mun. Code § 17-142(d); see also *803Colo. Rev. Stat. § 25-6-302 (2017) ("A mother may breast-feed in any place she has a right to be."). In that context, few would consider the sight of the woman's breast dangerous.
The need to protect children arises, instead, from the City's fear of topless women "parading in front of elementary schools, or swimming topless in the public pool"-scenarios that it described to the court at the preliminary-injunction hearing. Free the Nipple , 237 F.Supp.3d at 1131. But laws in the neighboring cities of Boulder and Denver, and in many other jurisdictions, allow female toplessness, and the City presented no evidence of any harmful fallout. Id. ; see also Boulder, Colo. Mun. Code § 5-6-13 (2017); Denver, Colo. Mun. Code § 38-157.1 (2017). In fact, the district court found, the City presented no evidence "that a law permitting public exposure of female breasts would have a significantly negative impact on the public." Free the Nipple , 237 F.Supp.3d at 1131. And absent contrary proof we, like the district court, doubt that without a female-toplessness ban on the books, topless women would "regularly walk[ ] through downtown Fort Collins," "parad[e]" past elementary schools, or swim in public pools. Id.
We're left, as the district court was, to suspect that the City's professed interest in protecting children derives not from any morphological differences between men's and women's breasts but from negative stereotypes depicting women's breasts, but not men's breasts, as sex objects. Id. ("[C]hildren do not need to be protected from the naked female breast itself but from the negative societal norms, expectations, and stereotypes associated with it."); cf. Tagami v. City of Chicago , 875 F.3d 375, 382 (7th Cir. 2017) (Rovner, J., dissenting) ("The City's claim therefore boils down to a desire to perpetuate a stereotype that female breasts are primarily the objects of desire, and male breasts are not."), cert. denied , --- U.S. ----, 138 S.Ct. 1577, 200 L.Ed.2d 747 (2018).
In support of this view, the district court relied on the testimony of Dr. Tomi-Ann Roberts, a psychology professor and witness for the Plaintiffs. At the preliminary-injunction hearing, Dr. Roberts testified that our society's sexualization of women's breasts-rather than any unique physical characteristic-has engrained in us the stereotype that the primary purpose of women's breasts is sex, not feeding babies. The district court found Dr. Roberts credible and concluded, based on her testimony, that "the naked female breast is seen as disorderly or dangerous because society, from Renaissance paintings to Victoria's Secret commercials, has conflated female breasts with genitalia and stereotyped them as such." Free the Nipple , 237 F.Supp.3d at 1133.
But laws grounded in stereotypes about the way women are serve no important governmental interest. Morales-Santana , 137 S.Ct. at 1692-93 ; Virginia , 518 U.S. at 550, 116 S.Ct. 2264. To the contrary, legislatively reinforced stereotypes tend to "create[ ] a self-fulfilling cycle of discrimination." Hibbs , 538 U.S. at 736, 123 S.Ct. 1972. Thus, the sex-object stereotype, according to Dr. Roberts, "serves the function of keeping women in their place." Appellant's App. vol. 3 at 192:11. And as the district court found, perpetuating the sex-object stereotype "leads to negative cognitive, behavioral, and emotional outcomes for both women and men." Free the Nipple , 237 F.Supp.3d at 1132. The court noted, for instance, that Dr. Roberts had testified about research linking the sexual objectification of women to the view that, at younger and younger ages, women are "appropriate targets of [sexual] assault." Appellant's App. vol. 3 at 194:22-23.
*804Accordingly, we reject the City's claim that protecting children from public nudity qualifies as an important governmental objective substantially served by the City's female-only toplessness ban.
ii. Maintaining Public Order and Promoting Traffic Safety
In the abstract, we agree that public order and traffic safety are important governmental objectives. The absence of either could be fatal. But the justification for a gender-based classification "must be genuine, not hypothesized," and "it must not rely on overbroad generalizations." Virginia , 518 U.S. at 533, 116 S.Ct. 2264. Here, we suspect that enacting the public-nudity ordinance had less to do with the City's professed objectives and more to do with the sex-object stereotype that the district court described. See Free the Nipple , 237 F.Supp.3d at 1132.
For one thing, in asserting that its female-only toplessness ban substantially furthers important governmental objectives, the City mostly relies on cases holding that nebulous concepts of public morality-not traffic safety or public order-justified similar bans. In one of those cases, for example, the Fourth Circuit tied a public-nudity ordinance like the City's to the "widely recognized" governmental interest in "protecting the moral sensibilities of that substantial segment of society that still does not want to be exposed willy-nilly to public displays of various portions of their fellow citizens' anatomies that traditionally in this society have been regarded as erogenous zones," portions that "still include (whether justifiably or not in the eyes of all) the female, but not the male, breast." United States v. Biocic , 928 F.2d 112, 115-16 (4th Cir. 1991) ; accord Tagami , 875 F.3d at 379 ; Ways v. City of Lincoln , 331 F.3d 596, 600 (8th Cir. 2003).
For another thing, although the City itself never asserted public morality as a justification for banning female toplessness, notions of morality may well underlie its assertions that conflicts will break out, and distracted drivers will crash, if it allows women to be topless in public. But such notions, like the fear that topless women will endanger children, originate from the sex-object stereotype of women's breasts. And as we've explained, that stereotype doesn't stand up to scrutiny. Cf. People v. Santorelli , 80 N.Y.2d 875, 587 N.Y.S.2d 601, 600 N.E.2d 232, 236 (1992) (Titone, J., concurring) ("One of the most important purposes to be served by the Equal Protection Clause is to ensure that 'public sensibilities' grounded in prejudice and unexamined stereotypes do not become enshrined as part of the official policy of government."); accord Obergefell v. Hodges , --- U.S. ----, 135 S.Ct. 2584, 2603, 192 L.Ed.2d 609 (2015) ; see also Planned Parenthood of Se. Penn. v. Casey , 505 U.S. 833, 850, 112 S.Ct. 2791, 120 L.Ed.2d 674 (1992) ("Our obligation is to define the liberty of all, not to mandate our own moral code.").
So what's left? A female-only toplessness ban strikes us as an unnecessary and overbroad means to maintain public order and promote traffic safety "when more accurate and impartial lines can be drawn." Morales-Santana , 137 S.Ct. at 1693 n.13 ; see also Craig , 429 U.S. at 208-09 & n.22, 97 S.Ct. 451 (striking down a gender-based differential in the age at which men and women could legally buy 3.2% beer because "the principles embodied in the Equal Protection Clause are not to be rendered inapplicable by statistically measured but loose-fitting generalities concerning the drinking tendencies of aggregate groups"). For instance, the City could abate sidewalk confrontations by increasing the penalties for engaging in offensive conduct. And to reduce distracted *805driving, the City could target billboards designed to draw drivers' eyes from the road. But the City can't impede women's (and not men's) ability to go topless unless it establishes the tight means-ends fit that intermediate scrutiny demands.
We recognize that ours is the minority viewpoint. Most other courts, including a recent (split) Seventh Circuit panel, have rejected equal-protection challenges to female-only toplessness bans. E.g. , Tagami , 875 F.3d at 380.8 But see id. at 383 (Rovner, J., dissenting) ("Whether out of reverence or fear of female breasts, Chicago's ordinance calls attention to and sexualizes the female form and imposes a burden of public modesty on women alone, with ramifications that likely extend beyond the public way." (citing Free the Nipple , 237 F.Supp.3d at 1133 ) ); Santorelli , 587 N.Y.S.2d 601, 600 N.E.2d at 237 (Titone, J., concurring) ("[T]he People have offered nothing to justify a law that discriminates against women by prohibiting them from removing their tops and exposing their bare chests in public as men are routinely permitted to do."). None of these decisions binds us, though; nor does their sheer volume sway our analysis.
As we interpret the arc of the Court's equal-protection jurisprudence, ours is the constitutionally sound result. At least since Virginia , that arc bends toward requiring more-not less-judicial scrutiny when asserted physical differences are raised to justify gender-based discrimination, while casting doubt on public morality as a constitutional reason for gender-based classifications. See, e.g. , Morales-Santana , 137 S.Ct. at 1689 (clarifying that "all gender-based classifications" are subject to "heightened scrutiny" (quoting J.E.B. , 511 U.S. at 136, 114 S.Ct. 1419 ) ); Virginia , 518 U.S. at 533, 116 S.Ct. 2264 (" 'Inherent differences' between men and women, we have come to appreciate, remain cause for celebration, but not for denigration of the members of either sex or for artificial constraints on an individual's opportunity."); Franklin, supra , at 145-46 ("[T]he Court's opinion [in Virginia ] suggests that equal protection law should be particularly alert to the possibility of sex stereotyping in contexts where 'real' differences are involved, because these are the contexts in which sex classifications have most often been used to perpetuate sex-based inequality.").
For these reasons, we believe that the district court correctly analyzed the Plaintiffs' equal-protection claim. The court didn't abuse its discretion in concluding that because the Plaintiffs made a strong showing of their likelihood of success on the merits, the first preliminary-injunction factor weighed in their favor.
B. The Second Factor: Irreparable Injury
The second preliminary-injunction factor asks whether irreparable injury will befall the movants without an injunction. Awad , 670 F.3d at 1131. Most courts consider the infringement of a constitutional right enough and require no further showing of irreparable injury. Id. ; accord Wright & Miller, supra , § 2948.1. The district court applied that principle here, concluding that the City's public-nudity ordinance inflicts irreparable harm by violating the Plaintiffs' right to equal protection under the *806law. See Free the Nipple , 237 F.Supp.3d at 1134.
On appeal, the City acknowledges that well-settled law supports the constitutional-violation-as-irreparable-injury principle. See, e.g. , Elrod v. Burns , 427 U.S. 347, 373-74, 96 S.Ct. 2673, 49 L.Ed.2d 547 (1976) ; Awad , 670 F.3d at 1131 ; accord Wright et al., supra , § 2948.1. And the City seems to concede that in the context of constitutional claims, the principle collapses the first and second preliminary-injunction factors, equating likelihood of success on the merits with a demonstration of irreparable injury. The City nevertheless contests its application here on the ground that neither the district court nor the Plaintiffs cited a decision analyzing the specific injury asserted here: an equal-protection violation from a prohibition on public nudity.
We're not persuaded. What makes an injury "irreparable" is the inadequacy of, and the difficulty of calculating, a monetary remedy after a full trial. Awad , 670 F.3d at 1131. Any deprivation of any constitutional right fits that bill. See Adams ex rel. Adams v. Baker , 919 F.Supp. 1496, 1504-05 (D. Kan. 1996) (concluding that excluding the plaintiff from the wrestling team because of her gender deprived her of her right to equal protection and that this deprivation "itself" constituted irreparable harm). Here, absent the preliminary injunction, the Plaintiffs, and all women in Fort Collins, risk criminal sanctions for making a choice-to appear topless in public-that men may make scot-free. See Fort Collins, Colo. Mun. Code § 17-142. We've already concluded that this gender disparity violates the Equal Protection Clause, so we agree with the district court that the Plaintiffs need to show no further irreparable harm.
Accordingly, we conclude that the district court didn't abuse its discretion in concluding that the Plaintiffs met the irreparable-injury requirement.
C. The Third Factor: The Balance of Harms
The third preliminary-injunction factor involves balancing the irreparable harms identified above against the harm that the preliminary injunction causes the City. Fish , 840 F.3d at 754. Under the heightened disfavored-injunction standard, the Plaintiffs need to make a strong showing that the balance of harms tips in their favor. Awad , 670 F.3d at 1131. When a constitutional right hangs in the balance, though, "even a temporary loss" usually trumps any harm to the defendant. Wright et al., supra , § 2948.2 & n.10. In this case, according to the district court, the Plaintiffs met their third-factor burden because the deprivation of their right to equal protection outweighed the stakes for the City, which the court defined as the public's interest in morality. Free the Nipple , 237 F.Supp.3d at 1134.
The City contests that conclusion on appeal, asking "how any injury [the Plaintiffs] might sustain from being required to wait to bare their breasts in public until after this matter is concluded outweighs the City's interest in maintaining a law that was supported by the majority of its citizens and unanimously adopted by its City Council." Appellant's Opening Br. at 35. But "being required to wait to bare their breasts in public" deprives the Plaintiffs of a constitutional right, while the City has no interest in keeping an unconstitutional law on the books. Cf. Awad , 670 F.3d at 1131 ("[W]hen the law that voters wish to enact is likely unconstitutional, their interests do not outweigh [a plaintiff's interest] in having his constitutional rights protected.").
*807For these reasons, we conclude that the district court didn't abuse its discretion in determining that the balance of harms tips in the Plaintiffs' favor, even under the "strong showing" standard applicable to disfavored injunctions.
D. The Fourth Factor: The Public Interest
The last preliminary-injunction factor requires that the injunction not be against the public interest. Awad , 670 F.3d at 1132. But as the district court wrote, it's "always in the public interest to prevent the violation of a party's constitutional rights." Free the Nipple , 237 F.Supp.3d at 1134 (quoting Connection Distrib. Co. v. Reno , 154 F.3d 281, 288 (6th Cir. 1998) ). On appeal, the City disputes that the public-nudity ordinance is unconstitutional, but it cites no law casting doubt on the public's interest in preserving constitutional rights. See Awad , 670 F.3d at 1132 ; see also Baker , 919 F.Supp. at 1505 ("The public interest would best be served by enjoining the defendants from infringing on the plaintiff's right to equal protection.").
As we explained above, the ordinance likely is unconstitutional, so we find the City's argument unconvincing. We conclude that the district court didn't abuse its discretion in ruling that the public-interest factor weighs in the Plaintiffs' favor.
* * *
In sum, because we agree with the district court that each preliminary-injunction factor favored the Plaintiffs, we also agree that the Plaintiffs should prevail on their preliminary-injunction motion. Thus, the district court didn't abuse its discretion in issuing the injunction.
CONCLUSION
For these reasons, we affirm the district court's order granting the Plaintiffs' motion for a preliminary injunction, and we remand the case to the district court for further proceedings consistent with this opinion.