This spring, he was auditioning to be the host of “Jeopardy!” Nearly every day, he pops up on television ads for national brands like State Farm insurance. And on Sundays this fall, he has led the Green Bay Packers to a division-best 7-2 record.

Quarterback Aaron Rodgers is not just the N.F.L.’s reigning most valuable player, he’s a celebrity who transcends the nation’s most popular sport, a household name on par with Tom Brady and Patrick Mahomes.

So when news broke that he tested positive for the coronavirus last week and was unvaccinated, Rodgers justified his decision to not get vaccinated by speaking out against the highly effective vaccines and spewing a stream of misinformation and junk science. Medical professionals were disheartened not just because it will make it harder for them to persuade adults to get vaccinated, but because they are also starting to vaccinate 5- to 11-year-olds.

“When you’re a celebrity, you are given a platform,” said Dr. Paul A. Offit, the director of the Vaccine Education Center at the Children’s Hospital of Philadelphia. “When you choose to do what Aaron Rodgers is doing, which is to use the platform to put out misinformation that could cause people to make bad decisions for themselves or their children, then you have done harm.”

The N.F.L. is investigating whether Rodgers and the Packers violated any of the league’s expansive Covid-19 protocols, which were developed with the N.F.L. Players Association. Rodgers admitted to flouting those protocols, including attending a Halloween party with teammates where he appeared in videos unmasked. The Packers and Rodgers could be fined hundreds of thousands of dollars for failing to adhere to the rules.

Rodgers is in the midst of a 10-day isolation period and did not play in the Packers’ 13-7 loss to Kansas City on Sunday. Like all unvaccinated N.F.L. players who test positive, Rodgers must provide two negative tests, taken 24 hours apart, after his isolation to return to the field, which could come as soon as Saturday.

The lasting damage from Rodgers’s stance, though, cannot be measured in dollars or games lost or won. Vaccination rates in the N.F.L. are very high compared to the general population. Nearly every coach and staff member who is around players is vaccinated, and 94 percent of the 2,000 or so players have also been inoculated, according to the league.

But given how popular the league is, even the handful of unvaccinated players get outsize attention. Wide receiver Cole Beasley of the Buffalo Bills, and quarterbacks Kirk Cousins of the Minnesota Vikings and Carson Wentz of the Indianapolis Colts have all been criticized for choosing to remain unvaccinated.

But they were upfront about their decisions. Rodgers, by contrast, evaded answering directly when asked if he was vaccinated. He said he was “immunized.”

In an interview on The Pat McAfee Show last week, Rodgers said he followed his own “immunization protocol,” though he did not provide details about what it entailed. But vaccination and natural infection are the only ways to gain immunity to the virus, scientists said.

In the interview, Rodgers fueled the controversy further by trying to distance himself from conspiracy theorists. “I’m not, you know, some sort of anti-vax, flat-earther,” he said. “I am somebody who’s a critical thinker.”

But many of his statements on the show echo those made by people in the anti-vaccine movement.

“Aaron Rodgers is a smart guy,” said David O’Connor, a virologist at the University of Wisconsin-Madison and a Packers fan. But, he added, “He’s still vulnerable to the blind side blitz of misinformation.”

In the interview, Rodgers suggested that the fact that people were still getting, and dying from, Covid-19, meant that the vaccines were not highly effective.

Although imperfect, the vaccines provide extremely strong protection against the worst outcomes of infection, including hospitalization and death. Unvaccinated Americans, for instance, are roughly 10 times more likely to be hospitalized and 11 times more likely to die from Covid-19 than vaccinated Americans, according to a study by the Centers for Disease Control and Prevention.

“As far as the people who are in the hospital with Covid, overwhelmingly, those are unvaccinated people,” said Angela Rasmussen, a virologist at the Vaccine and Infectious Disease Organization at the University of Saskatchewan. “And transmission is being driven overwhelmingly by unvaccinated people to other unvaccinated people.”

Rodgers also expressed concern that the vaccines might cause fertility issues, a common talking point in the anti-vaccine movement. There is no evidence that the vaccines affect fertility in men or women.

“Those allegations have been made since the vaccines first came on the scene, and they clearly have been addressed many, many times over,” said Dr. William Schaffner, a vaccine expert at Vanderbilt University. He added, “The vaccines are safe and stunningly effective.”

There are a few potentially serious adverse events that have been linked to the vaccines, including a clotting disorder and an inflammation of the heart muscle, but they are very rare. Experts agree that the health risks associated with Covid-19 overwhelmingly outweigh those of vaccination.

Rodgers said he ruled out the mRNA vaccines, manufactured by Pfizer and Moderna, because he had an allergy to an unspecified ingredient they contained.

Such allergies are possible — a small number of people are allergic to polyethylene glycol, which is in the Pfizer and Moderna vaccines — but extremely rare. For instance, there were roughly 11 cases of anaphylaxis, a severe allergic reaction, for every million doses of the Pfizer vaccine administered, according to one C.D.C. study.

The public health agency recommends that people with a known allergy to an ingredient in one of the mRNA vaccines not get those vaccines, but some scientists expressed skepticism that Rodgers truly had a known, documented allergy. Even if he did, he may have been eligible for the Johnson & Johnson vaccine, which relies on a different technology.

Rodgers also took aim at the N.F.L., almost daring the league to fine him. He claimed, for instance, that the league sent a “stooge” to the Packers’ training camp to “shame” the players into getting vaccinated. He said he did not follow some protocols, like wearing a mask when speaking with reporters, because he did not agree with them.

Like many star athletes, Rodgers has worked hard to shape his own narrative. But that can come at a cost, as the pushback to his comments has shown.

“The challenge for players now is it’s so easy for them to go on podcasts and tweet,” said Brad Shear, a lawyer who advises N.F.L. players on technology and social media. “I tell players to stay on script, have notes handy and when you get a tough question, deflect. His interview was like a car crash that got worse and worse.”

Though the league has no timeline for finishing its investigation, the blowback has been swift. Prevea Health, a primary care provider in Wisconsin, ended its partnership with Rodgers the day after his interview went public. State Farm, which has employed Rodgers as a spokesman for years, said it did not support some of the statements Rodgers made (without specifying which), but that it respects “everyone’s right to make a choice.”

On Sunday, just 1.5 percent of all televised State Farm ads included Rodgers, compared to around 25 percent the previous two Sundays, according to data collected by Apex Marketing, which monitors and tracks national media and branding.

Television commentators, including the Hall of Fame quarterback Terry Bradshaw, also called out Rodgers for potentially putting his teammates in jeopardy and not being honest. Basketball legend Kareem Abdul-Jabbar went one step further. “Aaron Rodgers didn’t just lie he also damaged professional sports,” he wrote.

Rodgers is no stranger to controversy. Through much of his 17-year N.F.L., he has created an image as a contrarian on a range of issues. In late April, ESPN reported that Rodgers was so “disgruntled” with the Packers that he told members of the team that he did not want to return to Green Bay. The team’s general manager, Brian Gutekunst, who was busy preparing for the draft, had to state publicly that Rodgers would not be traded.

Rodgers also used his knack for calculated disruption in 2020, when he tried to convince other players to vote against a proposed labor deal because it contained a path toward adding a 17th game to the regular season. (The players narrowly approved the agreement.)

Rodgers has made news not just because he is an elite quarterback, but because he’s an elite quarterback in the country’s most popular sports league. Every issue is magnified when the N.F.L. is involved, whether it is bullying, domestic violence, protests during the national anthem and other issues. That’s why Rodgers’s stance on vaccines has caused so much anxiety among scientists.

Dr. O’Connor said that he “cringed” when he heard that Rodgers had not been vaccinated, especially given how many people in Wisconsin have yet to get their shots; 63 percent of state residents have had at least one vaccine dose, compared to a 67 percent rate nationally.

“Within the community where he plays, there is still a lot of work to be done to improve vaccine uptake,” he said.

The timing, coming just as the vaccination campaign for young children gets underway, is particularly unfortunate, Dr. Schaffner said.

“He is such a highly regarded and highly admired sports figure,” he said of Rodgers. “We would want clear role modeling there to get the vaccine, and we certainly don’t want role modeling of duplicitous behavior.”