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.

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.

Ms. Ames sued under a federal civil rights law that forbids employment discrimination based on, among other characteristics, sex. (The Supreme Court ruled in 2020 that discrimination based on sexual orientation is a form of sex discrimination for purposes of the civil rights law.)

The text of the law, Title VII of the Civil Rights Act of 1964, does not draw distinctions based on whether the person claiming discrimination is a member of a majority group. But some courts have required such plaintiffs to prove an additional element if they lack direct evidence of discrimination: “background circumstances that support the suspicion that the defendant is that unusual employer who discriminates against the majority.”

Lower courts ruled against Ms. Ames on that ground. The U.S. Court of Appeals for the Sixth Circuit, in Cincinnati, said she could have satisfied the “background circumstances” requirement by showing decisions about her employment were made by “a member of the relevant minority group (here, gay people)” or with statistical evidence.

But the appeals court said Ms. Ames had provided neither kind of proof. (In the trial court, she said the two supervisors who took negative employment actions against her were straight. On appeal, she said a gay supervisor had also played a role. The appeals court ruled that she had forfeited that argument by not making it sooner.)

Conservative legal groups have championed Ms. Ames’s case. But the Biden administration too supported her argument, filing a brief supporting Ms. Ames.

At the argument on Wednesday, Ashley Robertson, a lawyer for the Trump administration, took the same position, rejecting the appeals court’s ruling. She said it amounted to this: “Tell me your race, and I will tell you how much evidence you need to produce.”

T. Elliot Gaiser, Ohio’s solicitor general, who represented the state agency that employed Ms. Ames, had the unenviable task of trying to win his case while disavowing the appeals court decision he was defending.

Mr. Gaiser said that “Ohio agrees it is wrong to hold some litigants to a higher standard because of their protected characteristics.”

Justice Elena Kagan was taken aback. She asked whether the appeals court was wrong.

Mr. Gaiser said yes. “The idea that you hold people to different standards because of their protected characteristics is wrong,” he said.

He said Ms. Ames could not meet the usual burdens on plaintiffs in employment discrimination cases. “She could not establish that anybody was motivated by sexual orientation or even knew her sexual orientation,” he said.

Several justices said those arguments should be addressed in the lower courts.

The only question the Supreme Court had agreed to decide, Justice Kagan said, “is whether a majority-group plaintiff has to show something more than a minority-group plaintiff, here, whether a straight person has to show more than a gay person.”

The parties in the case treated it as a technical matter largely unrelated to the broader debate over diversity programs that has long divided the public and has been amplified since the second Trump administration has made the elimination of diversity, equity and inclusion programs in government and the private sector one of its central projects.

But conservative legal groups filed supporting briefs taking aim at the notion that discrimination against white employees, straight people and men is in any way unusual.

“The rise of D.E.I. ideology and racial preferences means that discrimination is all too common today,” said a brief from the Pacific Legal Foundation, a libertarian group.

A brief from the NAACP Legal Defense and Educational Fund, on the other hand, said the justices should take account of Title VII’s history and purpose, which was focused on historically disadvantaged minorities. “The virtual absence of widespread discrimination targeting certain majority groups like white people and straight people,” the brief said, “is well documented, and it is a relevant and important consideration.”

Only Justice Samuel A. Alito Jr. touched on those issues, and only glancingly. “The rule that the Sixth Circuit applied was apparently based on an intuition about the way in which most employers behave,” he said, adding that the intuition may have made sense when a key precedent was issued in 1973 but may be “no longer sound today.”

Lawyers for local governments raised a different concern, saying that a ruling for Ms. Ames would produce “a looser standard that is all but certain to open the floodgates of litigation.”

Justice Amy Coney Barrett asked questions about what she called “a floodgate problem” but seemed satisfied by an answer from Xiao Wang, a lawyer for Ms. Ames.

More than half of the nation’s federal appeals courts do not require members of majority groups to meet a heightened burden, he said, adding that “we don’t see those circuits having some sort of flood of litigation.”