The Supreme Court heard arguments on Wednesday over an employment discrimination suit filed by a straight woman who twice lost positions to gay workers. The case comes 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.

While some conservative groups have hoped the case will yield a major statement on efforts to diversify the workplace, it seemed likely to produce a modest decision saying merely that a key civil rights law applied equally to all employees.

Indeed, the argument was notable for what Justice Neil M. Gorsuch called the “radical agreement” among not only justices across the ideological spectrum but also, remarkably, all of the lawyers in the case. They all said that an appeals court had gone badly astray in imposing a heightened burden for members of majority groups seeking to prove workplace discrimination.

The court seemed likely to issue a brief and perhaps unanimous decision in favor of the woman, Marlean A. Ames. Justice Brett M. Kavanaugh said he envisioned “a really short opinion that says discrimination on the basis of sexual orientation, whether it’s because you’re gay or because you’re straight, is prohibited, and the rules are the same.”

Ms. Ames 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, eventually giving the position to a gay woman who had been at the department for a shorter time and, unlike Ms. Ames, lacked a college degree.