At the bottom of the slope where snowboarders will compete in the 2022 Beijing Olympics, an electronic sign cycles through ads for companies like Samsung and Audi. Coca-Cola’s cans are adorned with Olympic rings. Procter & Gamble has opened a beauty salon in the Olympic Village. Visa is the event’s official credit card.

President Biden and a handful of other Western leaders may have declared a “diplomatic boycott” of the Winter Games, which begin next week, but some of the world’s most famous brands will still be there.

The prominence of these multinational companies, many of them American, has taken the political sting out of the efforts by Mr. Biden and other leaders to punish China for its human rights abuses, including a campaign of repression in the western region of Xinjiang that the State Department has declared a genocide.

The Olympic sponsorship reflects the stark choice facing multinational companies working in the country: Jeopardize access to an increasingly sensitive China, or deal with the reputational risk associated with doing business there. When it comes to the Beijing Olympics, the decision has been clear.

While the sponsors have faced protests by human rights activists in several countries, they have largely brushed them aside, choosing instead to keep China, and its emerging class of nationalistic consumers, happy.

The companies argue that the Olympics are not political, and that they have spent hundreds of millions of dollars on deals that span multiple Games, not just Beijing’s. Collectively, the top 13 Olympic sponsors have contracts with the International Olympic Committee that add up to more than $1 billion.

“They just seem to be proceeding as normal,” said Mandie McKeown, executive director of the International Tibet Network, a group that helped to organize protests by more than 200 rights groups calling for a boycott of the Olympics. “It’s literally like they’ve got their heads in the sand.”

For companies, though, the risk of angering Chinese consumers by criticizing China’s policies are high. Armies of patriotic voices on Chinese social media have furiously denounced foreign brands for perceived slights, vitriol often amplified by the government and official state media.

Adidas, Nike and other fashion companies faced nationwide boycotts in China after they expressed concerns about reports of forced labor in Xinjiang, the region where the Communist Party has forced millions of Uyghur Muslims into mass detention and re-education camps. When the fashion retailer H&M pledged to stop buying cotton from Xinjiang, a boycott by Chinese consumers cost it around $74 million in lost sales over one quarter.

Even one of the top Olympic sponsors, Intel, faced a backlash last month after the company posted a letter calling on international suppliers to avoid sourcing products from Xinjiang. In the face of the fury, Intel rewrote the letter within days to remove the reference to Xinjiang.

“The space to please both sides has evaporated,” said Jude Blanchette, a scholar at the Center for Strategic and International Studies in Washington. “When choosing who to upset, it’s either a bad week or two of press in the U.S. versus a very real and justified fear that you’ll lose market access in China.”

Top sponsors have sidestepped questions, at times awkwardly, about whether their support effectively whitewashes the Communist Party’s authoritarian rule. The Olympics, executives argue, should not be politicized, pointing to the Olympic Charter, which says as much, despite a long history of political intrigue surrounding the Games.

Only four major sponsors — Omega, Intel, Airbnb and Procter & Gamble — responded to requests for comment. Omega, the official timekeeper and data handler of the Olympic Games, said that since it started its partnership with the Olympic Games in 1932, “it has been our policy not to get involved in certain political issues because it would not advance the cause of sport in which our commitment lies.”

Airbnb and Procter & Gamble said they were focused on individual athletes and emphasized their commitment to each Olympics Games rather than Beijing, specifically. A representative at Intel said the company would “​​continue to ensure that our global sourcing complies with applicable laws and regulations in the U.S. and in other jurisdictions where we operate.”

“Ski and sport have no business in politics,” said Justin Downes, president of Axis Leisure Management, a hospitality company and contractor that is working with the Canadian Olympic Committee and others to help with logistics and supplies.

Almost all the Olympic sponsors have codes of ethics or a corporate social responsibility pledge to honor human rights, but these Games have tested how far they will go to speak out against widely recognized violations.

In China, those violations have included the crackdown in Xinjiang, as well as the continuing repression of Tibet, the erosion of political freedoms in Hong Kong and the threats to assert China’s territorial claim over Taiwan.

Mr. Downes has signed contracts with Olympics venues to ensure that the people he employs do not raise politically sensitive topics. If any member of his staff, which includes medical responders, makes a political statement on subjects like Xinjiang, Mr. Downes could be liable, he said.

“We are told not to disclose on certain topics or post pictures on social media,” Mr. Downes said of the contracts. “They don’t want people showing up and making a statement. It’s common sense.”

China’s critics say the sponsors have associated themselves with an event that could tarnish their brands. Some have compared these Games to the 1936 Summer Olympics in Berlin, which Nazi Germany used to showcase Hitler’s fascist regime.

“We always repeated these words, ‘Never again’,” said Tenzyn Zöchbauer, an ethnic Tibetan who has joined protests in Germany against Allianz, the insurance and financial services giant that is also a top Olympic sponsor. “At least genocide should be a red line,” she added, referring to China’s crackdown in Xinjiang.

For many international companies, however, the Winter Olympics are an opportunity to capture the attention of more than a billion consumers around the world, as well as inside China’s huge consumer market.

Beyond the top sponsors, numerous international companies have promoted their products in Olympic-themed campaigns. In one shopping center in Beijing, Adidas has erected a ski slope with skiing mannequins. At one Pizza Hut, the official panda mascot for the Games waves from a window display.

A skiing Bing Dwen Dwen, as the panda is known in China, is also splashed across KFC boxes.

The prominence of such advertising campaigns risks unwanted attention in the United States.

Executives from Coca-Cola, Airbnb, Intel, Procter & Gamble and Visa were hauled in front of Congress in July and accused of putting profits before ethics with their Olympics sponsorships. They have all been assailed in public letters. Lawmakers in the United States and in Europe have called them out for participating.

Even so, the issue of human rights violations in China has not generated enough protests to threaten the profits of multinational companies, while the angry Chinese consumers have fueled painful boycotts.

“Let’s be honest — nobody, nobody cares about what’s happening to the Uyghurs, OK?” Chamath Palihapitiya, the billionaire investor and part-owner of the National Basketball Association’s Golden State Warriors, said this month. Mr. Palihapitiya was criticized for the remark, and the Warriors later played down his involvement with the team.

Of the top Olympic sponsors, only Allianz is known to have met with activists calling for a boycott of the Games. The company has not spoken out, however. A protest last week at the doors of its office in Berlin drew only seven people.

Many of the main sponsors appear to be hoping they get through the Olympics without drawing too much attention.

Activists say the sponsors and the International Olympic Committee have the economic leverage to influence the Chinese authorities but are too timid to wield it.

“If any other government in the world did what the Chinese are doing in Xinjiang or even in Hong Kong, a lot of companies would just pull up stakes,” said Michael Posner, a former State Department official who is now at New York University’s Stern School of Business.

He cited decisions by companies to divest in places like Myanmar and Ethiopia, as well as the campaigns to boycott South Africa when its apartheid government sent all-white teams to the Olympics.

“China is an exception,” he said. “It’s just so big, both as a market and a manufacturing juggernaut, that companies feel they can’t afford to get in the cross hairs of the government, so they just keep their mouths shut.”

Claire Fu contributed research. Keith Bradsher contributed reporting.