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 and gestured with his fingers in the air to indicate quotation marks around the word “immunized,” a suggestion that he was trying to be ironic.

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.”