The Supreme Court on Thursday unanimously ruled in favor of a straight woman who twice lost positions to gay workers, saying an appeals court had been wrong to require her to meet a heightened burden in seeking to prove workplace discrimination because she was a member of a majority group.

The decision came two years after the Supreme Court struck down race-conscious admissions programs in higher education and amid the Trump administration’s fierce efforts to root out programs that promote diversity and could make it easier for white people, men and other members of majority groups to pursue claims of employment discrimination.

The standards for proving workplace discrimination under a federal civil rights law, Justice Ketanji Brown Jackson wrote for the court, “does not vary based on whether or not the plaintiff is a member of a majority group.”

The case was brought by Marlean A. Ames, who had worked for the Ohio Department of Youth Services, which oversees parts of the state’s juvenile corrections system. After a decade there, in 2014 she became the administrator of a program addressing prison rape. Five years later, she applied for a promotion.

Her supervisors turned her down, saying she lacked vision and leadership skills. They eventually gave the position to a gay woman who had been at the department for a shorter time and, unlike Ms. Ames, lacked a college degree.

Not long after denying her the new position, her supervisors removed her from her existing job, telling her that they had concerns about her leadership and offering her a demotion that came with a substantial pay cut. She was replaced by a gay man with less seniority.