In a less dangerous time, a more forgiving public viewed Novak Djokovic’s nontraditional views of science and health as the quirky characteristics of a hyperactive seeker with strongly held beliefs about everything from sports to spirituality.

He has sat inside a pressurized, egg-shaped pod during major tournaments, believing it would improve circulation, boost his red-blood cell production and rid his muscles of lactic acid. He said that prayer and faith could purify toxic water. Djokovic and other high-profile athletes with unorthodox approaches to health were a source of bemusement for a public that, for better or for worse, has long treated them as role models. These quirks as seemingly harmless as a bowl of quarterback Tom Brady’s avocado ice cream.

Not anymore.

Djokovic, an outspoken skeptic of vaccines, will spend the weekend detained in a hotel room in Melbourne, Australia, waiting out a legal appeal and expected hearing on Monday in hopes of gaining entry to the country following a public and political outcry over the medical exemption he received to play in the Australian Open without being vaccinated. The Australian Border Force rejected his paperwork supporting that exemption on Wednesday.

The pitched battle over what was supposed to be his quest for a record 10th Australian Open men’s singles championship has highlighted a new dynamic for stars like Djokovic. The latest surge of coronavirus cases and the ongoing struggle to exit the pandemic have shifted public perceptions: athletes once viewed favorably as iconoclasts are now encountering pushback when they want to play by different rules than everyone else.

“The general public continues to respond positively if an athlete is speaking out on topics that make a difference in society and make peoples lives better,” said Michael Lynch, the former director of sports marketing for Visa and a longtime consultant to the sports industry. “But if someone takes a position that put peoples’ lives at risk, then they are going to have very negative reaction.”

The fame that comes with athletic success has provided Djokovic and other top athletes who oppose the coronavirus vaccines, like the N.F.L. quarterback Aaron Rodgers and the star basketball player Kyrie Irving, with platforms to promote causes they believed in and to collect millions of dollars to promote products. But in recent months, their high profiles have become a liability as their behavior and their views supported misinformation and put public safety at risk.

For sports organizations and leagues, the stakes are high. For more than a decade, access to social media has given sports stars the ability to become more outspoken and impactful than ever. As long as what they say has not been offensive or polarizing, they provided free, mostly positive publicity for their sports, their causes and their own brands.

The vaccination issue has changed the equation for sports, whose return in 2020 was viewed positively when they modeled safe behavior, such as mask wearing, playing before sparse crowds or no one at all, and participating in regular testing. The behavior and outspokenness of Djokovic, Rodgers, Irving and others against vaccines has jeopardized that good will, and organizations are now tightening their rules to play defense.

The N.C.A.A. said on Thursday that, in many instances, it would not consider players or coaches “fully vaccinated” unless they had also received a booster shot.

Although the guidance is not binding on schools and conferences, it is influential, especially with the N.C.A.A.-run Division I basketball tournaments scheduled to begin in March.

“You’re allowed to have your own beliefs but once those beliefs start to impact other people, that is where things begin to get a little dodgy,” said Patrick McEnroe, the former professional tennis player who is now a commentator for ESPN.

That dynamic came to a head in Australia on Wednesday when federal border police detained Djokovic at a Melbourne airport.

Djokovic, a Serb who has won 20 Grand Slam tournament singles championships, had flown to Australia to defend his title in the Australian Open following the announcement that he had received a medical exemption from receiving a vaccine for an undisclosed reason from two panels of medical experts working on behalf of the organization that stages the tournament and the government of Victoria, the state that includes the tournament site, Melbourne. But while Djokovic was en route to Australia from Dubai, the public and some politicians began to voice their anger that Djokovic, No. 1-ranked men’s tennis player, had received unjustified special treatment.

Roughly 80 percent of Australians have received at least one dose of a vaccination. Australians have endured some of the most stringent prohibitions to prevent the spread of the virus, including lockdowns that lasted hundreds of days and strict limits on travel. With the country averaging roughly 30,000 new cases a day, Australians were no longer willing to tolerate an outspoken critic of vaccines getting a questionable special pass.

Border officials, with the support of Prime Minister Scott Morrison and other top federal officials, subsequently rejected his efforts to enter Australia on the grounds that his medical exemption was not valid.

Michael Payne, the former chief marketing officer for the International Olympic Committee, said Djokovic had gotten “caught in political power play between different government departments who should have told him upfront, ‘no vaccine, no play.’”

Perhaps, but Djokovic also could have avoided his troubles by simply getting vaccinated, as hundreds of millions of people have done during the past 12 months, either because they wanted to follow public health guidance or because employers or governments required it.

Same for Irving, the Nets guard who has steadfastly refused to get vaccinated. Irving’s refusal has made him ineligible to play in the Barclays Center in Brooklyn, because New York City requires people working indoors to be vaccinated.

The Nets had kept him off their roster for the first two months of the season. Then, as their losses mounted, the team opted to essentially make him a part-time employee who will play only in arenas in cities that don’t prohibit unvaccinated people from working indoors.

He scored 22 points Wednesday night in his first game of the season against the Indiana Pacers, but he will continue to be a symbol of everything the N.B.A. has tried to avoid during the pandemic, which is being seen as a potential danger to the public, which has dwindling patience for anyone who may be hindering efforts to end the pandemic.

Meanwhile, Rodgers, who is a folk hero in the Midwest, has the Green Bay Packers one win away from securing the top seed in the N.F.C. for the playoffs, which begin next week. Rodgers was criticized and ridiculed in November, when he tested positive for Covid-19 after months of making misleading statements about whether he was vaccinated. He also violated N.F.L. rules for unvaccinated players, including not wearing a mask while he was speaking with journalists. He missed a game while isolating and recovering from his illness. The N.F.L. fined the Packers $300,000 for enabling his behavior.

Rodgers explained his decision to not get vaccinated by saying he had read hundreds of pages of studies and received treatments to prevent infection, treatments that scientists have either debunked or have not been proven effective, including a veterinary drug. He quickly became an object of widespread scorn then blamed cancel culture for his treatment.

The star vaccine resistors do have their supporters. Djokovic’s family on Thursday held rallies in Belgrade, where his father, Srdjan, accused Morrison, the Australian prime minister, of holding his son “captive” for his beliefs and trampling on all of Serbia, where Djokovic is a hallowed treasure.

He also read a message that he said was from Djokovic: “God sees everything. Moral and ethics as the greatest ideals are the shining stars towards spiritual ascension. My grace is spiritual and theirs is material wealth.”

Djokovic’s chief rival, Rafael Nadal, who is in Australia ahead of playing in the Open, offered a less-than-sympathetic take on the dispute Thursday.

“In some way I feel sorry for him,” said Nadal, who has long supported vaccine efforts. “But at the same time, he knew the conditions since a lot of months ago, so he makes his own decision.”

Alan Blinder contributed reporting.