This October, the Supreme Court will officially weigh in on whether transgender people can be provided legal protection on the basis of sex—and in doing so, could decide the fate of how women of all kinds must dress in workplaces everywhere.

Aimee Stephens had worked as a funeral director for R.G. & G.R. Harris Funeral Homes Inc. in Garden City, Michigan for six years when she was fired in 2013, after she began to wear women’s clothing to work. According to an ACLU brief submitted to the Court, she lost her job when she transitioned—without federal protection against anti-transgender discrimination, Stephens would have to rely on state law to protect her. However, Michigan doesn’t outlaw such an offense. The Equality Act currently waiting for movement past the House would establish this protection, but the greatest legal recourse Stephens has is Title VII of the 1964 Civil Rights Act. Her legal challenge against her old employer will determine whether transgender people will be protected from sex discrimination in the workplace, an issue that has been heavily debated for years.

Discrimination on the basis of sex is prohibited under Title VII of the 1964 Civil Rights Act. Numerous lower court rulings have maintained that Stephens’ gender identity would be protected as it applies to “sex” under Title VII. But a Supreme Court ruling in Stephens’ favor would set that precedent at the highest level of our nation’s judiciary, establishing a landmark ruling for the transgender civil rights movement. Trans rights ought to be meaningful enough on their own to merit public concern, but it’s worth noting that government-sanctioned discrimination against trans Americans at work would have severe consequences for cis women, too.

If the conservative-majority Supreme Court rules against Stephens, the result would be devastating to the estimated 1.4 million trans people in the U.S.—particularly trans women of color, who are already unemployed at four times the rate of the general population. Now imagine how the rule could be applied to all women: Stephens was fired for her supposed inherent inability to conform to her employer’s subjective perspective on what women at work should look like, so if the Supreme Court says that’s legal, every woman in the United States may then also be forced to conform to an employer’s subjective, stereotyped idea of how a woman should look at work if she wants to keep her job. Hopefully she doesn’t look too much like a man in the opinion of her employer. Title VII covers gender stereotyping—the case of Ann Hopkins, who was denied partner at her firm in the 1980’s, established that expanded understanding of the law. (Hopkins’ case was later cited by the Obama Administration as one of many rulings to support its move to clarify that gender identity is protected under Title VII as an aspect of sex.)

In an earlier, lower court hearing on this case cited by the ACLU, Stephens’ employer, funeral home owner Thomas Rost testified that he has “yet to see a man dressed up as a woman that I didn’t know was not a man dressed up as a woman,” explaining that trans women’s supposed inability to look like women makes it impossible for such a person to meet the standards of his business’s dress code for female employees. “There is no way that… [Ms. Stephens] would be able to present in such a way that it would not be obvious that it was [a man],” Rost testified.

ACLU staff attorney Chase Strangio, a central figure in the legal battle for trans rights, brought up on Twitter this week, a ruling against Stephens would enable “employers to lawfully force women to wear skirts to work.”

“This case could turn back the clock on equality for everyone, not just LGBTQ people,” Strangio told VICE. The implication: This precedent could pave the way for employers to enforce archaic gendered dress codes akin to those of the 1950s, or whatever fits their expectations of gender expression. The Funeral Home claims that any prior ruling prohibiting sex-stereotyping is irrelevant because those rulings “don’t apply to trans people,” and says that “a trans woman like Ms. Stephens could never meet a gendered dress requirement—and therefore never fit into the workplace generally,” Strangio explained.

Follow that logic to its end. If the Supreme Court agrees, it will have established precedent that employers are allowed to make up their own gender-specific policies based on their personal beliefs about how men and women should look and behave. “The Court is poised to make a critical ruling on the nature of sex discrimination that will impact cis people, particularly cis women, in all aspects of life, particularly the workplace,” Strangio said.