LANCASTER, Pa. — On a blustery morning last month, Gerald Groff drove through rolling farmland in Amish country, slowing to pass the occasional horse-drawn buggy and pointing out some of the hundreds of mailboxes that used to mark his postal route.

Mr. Groff, a soft-spoken evangelical Christian and former missionary, said that delivering the mail was an arduous but noble calling. “Remember that this started with the Pony Express,” he said. “It’s written in the Constitution.”

But after the U.S. Postal Service struck a deal with Amazon in 2013 to deliver packages on Sundays, Mr. Groff said he faced a choice: to work on his Sabbath or lose his livelihood. “I’m put into a situation where I have to choose to honor my earthly authority or do what I know is right to honor God,” he said. “I have to choose God.”

On Tuesday, the Supreme Court will hear arguments on whether the Postal Service should have done more for Mr. Groff under Title VII of the Civil Rights Act of 1964, a federal law that requires employers to “reasonably accommodate” workers’ religious practice so long as they can do so “without undue hardship” to the company’s business.

The Supreme Court has lately been exceptionally receptive to claims of religious discrimination, largely from Christians, meaning that Mr. Groff’s prospects are good. A ruling in his favor would extend a remarkable run of decisions chipping away at the wall between church and state and expanding the role of religion in public life, sometimes at the expense of other values, like gay rights and access to contraception.

Mr. Groff’s case has the potential to affect countless workplaces and could require many employers to make major changes to accommodate religious workers. But a decision in his favor may be less contentious than some of the court’s recent rulings on religion, in part because protecting the Sabbath may not divide Americans along the usual fault lines. Indeed, liberal justices have been at the forefront of efforts to shield workers from discipline and termination for following their faith.

Rachel Laser, the president of Americans United for Separation of Church and State, said the case is “a wolf in sheep’s clothing.”

“Our civil rights laws rightly require religious accommodations for workers, which is especially important for religious minorities whose rights and customs might not be respected in the workplace,” she said. “But religious freedom does not mean we can shift the burden of practicing our faith onto other people. Religious freedom has never been a license to harm others, in employment or any other facet of life.”

Mr. Groff, 45, said his request was both modest and important.

“Sunday’s a day where we get together and almost taste heaven,” he said. “We come together as believers. We celebrate who we are, together. We worship God. And so to be asked to deliver Amazon parcels and give all that up, it’s just really kind of sad.”

In the last few years, the Supreme Court has ruled that a high school football coach had a constitutional right to pray at the 50-yard line after his team’s games, that state programs supporting private schools in Maine and Montana must include religious ones, that a Catholic social services agency in Philadelphia could defy city rules and refuse to work with same-sex couples who apply to take in foster children and that the Trump administration could allow employers with religious objections to deny contraception coverage to female workers.

The court’s three most conservative members — Justices Clarence Thomas, Samuel A. Alito Jr. and Neil M. Gorsuch — have already indicated that they may be prepared to overrule the key precedent in Mr. Groff’s case, Trans World Airlines v. Hardison. In that 1977 decision, the Supreme Court defined “undue hardship” narrowly, ruling that it applied to any accommodation that imposed more than a small, or “de minimis,” cost on the employer.

Mr. Groff’s superiors noted that his job, as a rural carrier associate, was to substitute for full-time workers and that he knew from the outset that it required flexibility and weekend work.

That did not pose a problem before the Amazon deal, as the post office had generally never delivered mail on Sundays. After the deal, Mr. Groff’s bosses made some accommodations but contended that allowing him to skip work on all Sundays was a significant burden, in tension with an agreement with a labor union and bad for other workers’ morale.

Over time, they disciplined him for failing to report for Sunday deliveries, and in 2019 he quit.

“I really didn’t want a federal termination to follow me the rest of my life,” Mr. Groff said. “So I went ahead and submitted a resignation because the harassment on a daily basis just got to the point where I couldn’t handle it anymore.”

He sued under the Civil Rights Act, and lower courts ruled against him. Judge Patty Shwartz, writing for a divided three-judge panel of the U.S. Court of Appeals for the Third Circuit, in Philadelphia, said that “exempting Groff from working on Sundays caused more than a de minimis cost on U.S.P.S. because it actually imposed on his co-workers, disrupted the workplace and work flow, and diminished employee morale.”

In dissent, Judge Thomas M. Hardiman wrote that “the majority renders any burden on employees sufficient to establish undue hardship, effectively subjecting Title VII religious accommodation to a heckler’s veto by disgruntled employees.”

Much has changed since the Supreme Court’s decision in the Hardison case in 1977, when religious liberty was largely a liberal cause and when the typical plaintiff was a member of a religious minority. In the Hardison case, involving an adherent of the Worldwide Church of God who wanted to observe a Saturday Sabbath, the two dissenting justices were liberal lions.

Justice Thurgood Marshall, joined by Justice William J. Brennan Jr., wrote that the “de minimis” standard adopted by the majority “makes a mockery of the statute,” adding that plain English did not support that interpretation of the phrase “undue hardship.”

The sums at issue in 1977 were “far from staggering: $150 for three months,” Justice Marshall wrote, adding: “To conclude that TWA, one of the largest air carriers in the nation, would have suffered undue hardship had it done anything more defies both reason and common sense.”

He called on the court to reverse course. “All Americans will be a little poorer until today’s decision is erased,” he wrote.

Mr. Groff is represented by First Liberty Institute, which says it is the largest legal organization in the nation focused exclusively on defending religious freedom. The group’s Supreme Court brief urged the justices to give the statutory “undue hardship” standard more bite.

The brief suggested borrowing a test used in cases under civil rights laws like the Americans With Disabilities Act, one that requires employers to provide an accommodation unless it would impose significant difficulty or expense considering the employer’s resources, the number of people who work for it and the nature of its business.

The Biden administration, representing the Postal Service, walked a fine line in its own Supreme Court brief in the case, Groff v. DeJoy, No. 22-174, saying that the court should stop short of overruling Hardison “while also clarifying and reinforcing its limits.”

The right place to draw the line, Solicitor General Elizabeth B. Prelogar wrote, was to say that employers need not operate short-handed or regularly pay overtime to replacement workers but must bear more modest costs like occasional overtime or the expenses associated with rearranging schedules.

Allowing Mr. Groff to observe the Sabbath would impose excessive costs, Ms. Prelogar added, saying that even the accommodations the Postal Service had made “actually contributed to other employees quitting or transferring.”

The Postal Service “has suffered substantial losses for many years,” she wrote, and the Amazon deal was critically important.

Mr. Groff, showing a visitor the post office where he used to work, said there must be a middle ground. He added that he missed his old job.

“I loved it,” he said. “I planned to make a career of it.”