PULLMAN, Wash. — With the leaves beginning to turn and the chilly air snapping skin to attention, Washington State’s football players awoke Saturday to a crisp fall morning. Walking into Martin Stadium through a gantlet of fans, parents, cheerleaders and a marching band only amplified their anticipation.

The morning, though, carried a different air for Nick Rolovich, the team’s coach. He woke up to unsettling news: that his former college coach, June Jones, told USA Today of Rolovich’s decision to apply for a religious exemption to a requirement that Washington state employees become vaccinated from the coronavirus. It was something he had hoped would remain private.

“I’m not terribly happy with the way it happened,” said Rolovich, who confirmed the report after his Cougars hung on for a 31-24 upset of Oregon State. Rolovich, who declined an interview request, spoke at a news conference. “I hope there is no player I coached that has to wake up and feel the way I felt today,” he said.

The victory kept his team afloat in the Pac-12 North Division race and sent a homecoming crowd of 24,157 off celebrating after Oregon State (4-2) was stopped at the 5-yard line in the final minute. But if Washington State (3-3) is in the news this season, it is likely to be less about its spirited play than about Rolovich, the only major-college football coach who has publicly refused to be vaccinated.

He announced it in July, and it prevented him from attending the Pac-12’s media day in person. He has repeatedly declined to elaborate, saying it is a private matter.

When Gov. Jay Inslee announced in August that state employees had to be vaccinated or receive a medical or religious exemption to keep their jobs, Rolovich, the state’s highest paid worker, remained resolute.

When Kirk Schulz, the university’s president, required that students be vaccinated before they could register for spring classes or that fans, starting Saturday with the Oregon State game, would need to have proof of vaccination or a negative virus test to attend home games, Rolovich’s position stood in even starker relief.

As the Cougars played on Saturday, a message across the street on the basketball arena’s marquee flashed: “Get vaccinated.”

“It certainly skews the perception of our message,” Schulz said in an interview on Friday. “At most universities, people pay attention to what the university president, the football coach, the basketball coach and the athletic director have to say — that’s just the reality. People look at them for leadership because they’re highly visible and highly compensated. It doesn’t help when you have people who are contrary to the direction we’re going.”

Schulz said the subject had come up “hundreds of times” in recent weeks in meetings with students, faculty, alumni or politicians. “It’s the No. 1 question,” he said. “It’s on everybody’s mind.”

The question now is whether Rolovich’s stance will cost him his job.

The governor’s decree requires state employees to be fully vaccinated — or receive an exemption — by Oct. 18, next Monday.

Rolovich’s is one of 437 requests for a religious exemption by university employees, 98 of which had been granted as of Friday. Rolovich said Saturday that he had not heard whether his request — which will be reviewed blindly, without his name or department — had been approved.

If the exemption is denied, he could appeal, be vaccinated or be fired.

If an exemption is granted, the employee’s supervisor must determine if the employee can still do the job effectively. For example, a university spokesman said, a graphic artist who works alone could be accommodated. Could a football coach conduct his required duties — meet with his team, run practice, host recruits, socialize with boosters and speak with reporters — without endangering others?

Making the determination would be Pat Chun, the athletic director who hired him, and who has career ambitions beyond his post in Pullman.

“I don’t think it’s a judgment call,” Chun said Friday at a homecoming pep rally, citing a process the university has laid out with guidance from the state attorney general’s office.

Rolovich, 42, is in the second year of a five-year contract that pays him $3 million per year before incentives. If he is fired without cause, the university would owe him $3.6 million after this season, under the terms of his contract — not pocket change for an athletic department that is hoping to whittle its debt to $77 million by the end of the fiscal year.

The university could fire him for not being able to fulfill the terms of his contract, but that might invite a lawsuit, along with ire of some boosters.

“If they fire him, I’m done supporting them — done,” Mark Wieseler of Pasco, Wash., said Saturday as he prepared to grill lamb chops for a tailgate party. He said he gives $25,000 to the athletic department each year.

Others are upset the issue is lingering over the team. “It’s selfish,” Blake Jones, who lives in Spokane, said as he and friends played cards and nursed beers outside an RV on Friday night. “Coaches complain about distractions. Well, he is the distraction.”

Still, the question at the heart of every conversation about Rolovich is: Why?

There have been police officers, nurses, doctors and others who have lost their jobs after refusing to be vaccinated, but few stand to lose as much money as Rolovich.

“He’s a different cat,” said Rich Miano, a former N.F.L. defensive back who coached alongside Rolovich when they were assistants at Hawaii and when Rolovich played there. “I never felt like I knew why he did things or what his intentions were. The $3 million question is whether he’ll chance getting fired for something we think he believes in or if he’ll string it out to the finish line. Most people here think he’s crazy.”

Washington State’s isolation, tucked among the winter wheat and lentil fields in the arid southeastern corner of the state, has made it a comfortable home for football coaches with an iconoclastic streak.

Wisecracking Mike Price, who walked around campus like Elmer Fudd in a duck-hunting outfit the week of a big game against Oregon, took the Cougars to two Rose Bowls — their only ones since 1930. Price was fired before ever coaching a game at Alabama for visiting a strip club.

And Mike Leach, the boundary-pushing coach with a law degree, an affinity for pirates and a sling-it-on-every-down offense, went to six bowls in eight seasons. (But Leach didn’t always endear himself to everyone here; Schulz said donors withdrew $4.5 million in pledges after Leach, who has campaigned for Donald J. Trump, tweeted a doctored video of a Barack Obama speech.)

Rolovich arrived here with a similar profile.

He became a folk hero in Hawaii after throwing eight touchdown passes as an injury replacement to ruin Brigham Young’s unbeaten season. He set aside plans to follow in his father’s footsteps as a firefighter and went into coaching, eventually turning the Rainbow Warriors around in his four seasons — and doing so with a carnival barker’s flair.