BEIJING — When the figure skater Nathan Chen won an Olympic gold medal for the United States, the state media in China, his parents’ birthplace, practically ignored his victory.

When the Californian-born skater Beverly Zhu stumbled on the ice in her first appearance for China, Chinese social media users told her to “go back to America.”

When Eileen Gu won gold skiing for China, people in China celebrated her as the nation’s pride. But in the United States, where she was born and trained, some conservative political pundits called her ungrateful.

To be an American-born athlete of Chinese descent on sport’s most prominent global stage is to be a lightning rod for patriotic, some say nationalistic, sentiment. Once held up as bridges linking the two countries, the Chinese American Olympians — and their successes and failures — are increasingly being seen as proxies in the superpowers’ broader geopolitical tussle.

In China, a resurgent nationalism has meant that even among citizens, anyone airing even the mildest of criticisms can be accused of disloyalty. But the scrutiny of Chinese Americans is often harsh in other ways.

They are expected to show loyalty as part of a perceived extended Chinese family, yet are also distrusted as outsiders. Depending on the moment and mood, they can be shunned as traitors to the motherland or embraced as heroes who bring glory to the nation.

For the athletes, choosing which country to compete for is often a personal or practical decision. Having ties to both the United States and China is also natural for Chinese Americans, many of whom grow up straddling two cultures, geographies and languages.

“When I’m in China, I’m Chinese and when I go to America, I’m American,” Ms. Gu, 18, has often said in response to questions about her decision to compete for China. Ms. Gu, whose father is white and mother is Chinese, was born and raised in California by her mother. She speaks Chinese fluently and visited Beijing frequently as a child.

But worsening geopolitical tensions between Beijing and Washington have made maintaining the balancing act difficult for such athletes.

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“We can see the heightened expectations and demands for these young athletes to pick a side, to prove their loyalty in one way or another,” said Ellen Wu, an associate professor of history at Indiana University who researches Asian American history.

Many countries have for decades recruited foreign-born athletes to boost their chances of winning medals at the Olympics. Now China, too, is looking abroad for talent as well.

Around 30 athletes competing for China in this year’s Games are naturalized Chinese citizens, with most playing for the men’s and women’s ice hockey teams. None, though, have attracted as much scrutiny in the United States as Ms. Gu, who has already won two medals at these Games.

Ms. Gu has said her decision to compete for China was driven by a desire to grow the sport in the country. She has thanked both the United States and China for grooming her. But some commentators on both sides are treating the Olympics like a battlefield and using rhetoric about “betrayal” and “loyalty” to describe the athletes.

Will Cain, a Fox News Host, said it was “ungrateful” of Ms. Gu to “betray the country that not just raised her, but turned her into a world-class skier.”

In China, however, Ms. Gu has quickly become a superstar. Many Chinese obsess over her strong Beijing accent, her success as a model and reports about her near-perfect SAT scores. She has a bevy of lucrative endorsements from top Chinese brands, like JD.com, Bank of China and Anta.

Despite the outpouring of adulation in China, Ms. Gu is also walking a fine line. She has so far declined to answer repeated questions about whether she surrendered her United States passport. (China does not allow dual nationality.)

Hu Xijin, a recently retired editor of Global Times, a brashly nationalist Chinese newspaper, warned Chinese propaganda organs on Sunday to moderate their praise of Ms. Gu, suggesting it was unclear which nation she would identify with as she got older.

“China’s national honor and credibility cannot be put at stake in the case of Gu Ailing,” he wrote, referring to Ms. Gu by her Chinese name.

The implication is that heritage alone is no longer enough for Chinese American athletes to be embraced by China. Rather, it now hinges on their ability to hew to China’s increasingly demanding, some say unrealistic, expectations.

Not being able to speak Chinese fluently was the first strike against Beverly Zhu, the California-born figure skater who competes for China under the name Zhu Yi. Then, she fell several times during competition, prompting Chinese social media users to unleash a wave of attacks against her, many of them ugly.

Many online users called her a “disgrace” and suggested — without evidence — that Ms. Zhu had been given a spot on the Chinese Olympics team over a Chinese-born skater because of the prominence of her father, a computer scientist who relocated to Peking University from the United States. The attacks were so intense that Chinese internet censors stepped in to tamp down the vitriol.

The negativity partly stems from a disillusionment with the United States and a perception in China that Washington is unfairly fanning hostility toward Beijing to try to block the country’s rise.

“There was a time when people felt it was awesome to be American,” said Hung Huang, a Chinese-born American writer based in Beijing. “But as politics between the two countries have spiraled down the rabbit hole, Chinese feel that they should not — or cannot — admire a country that point fingers at them all the time.”

The Chinese response to some of the athletes has been indifferent at best, derisive at worst. Last week, Chinese state media was noticeably silent on the gold medal win by Mr. Chen, the American figure skater, in the men’s individual event, focusing instead on Japan’s Yuzuru Hanyu, who finished fourth, and on the Chinese figure skater Jin Boyang, who placed ninth. Chinese social media users posted comments dismissing the American athlete’s achievement as unworthy of attention because, in their view, he had insulted China.

Mr. Chen had initially rankled the Chinese public at the 2018 Games, when he skated to the music of “Mao’s Last Dancer,” a 2009 film about a Chinese ballet dancer who had defected. (Mr. Chen said last week that he was not aware of the broader context of the music when he chose it.)

Then, in October, Mr. Chen drew more criticism in China when he supported his teammate, Evan Bates, in expressing concern about China’s human rights record.

“I agree with what Evan was saying,” Mr. Chen said at the time. “I think for a greater change to occur, there must be power that is beyond the Olympics. It has to be change at a remarkable scale.”

Two decades ago, China held up athletes like the figure skater Michelle Kwan and the tennis player Michael Chang as cultural ambassadors.

David Zhuang, a Chinese-born table tennis player competing for the United States, recalled receiving a raucous welcome when he returned to Beijing in 2008 for the Summer Olympics. Mr. Zhuang, who had moved to the United States in 1990, said in a phone interview that during one match he played, a group of Chinese fans gathered around and shouted encouraging words.

“Can you imagine, I had left the country 18 years before and here they were cheering me on,” recalled Mr. Zhuang. “I couldn’t play after that, I was so emotional.”

Watching the Games this time around, he said, the atmosphere felt completely different.

“When I look at the relationship today, and the politics and the competition between the two countries, it kind of hurts,” Mr. Zhuang said. “What a pity.”

Li You contributed research.