BEIJING — For international companies looking to do business in China, the rules were once simple. Don’t talk about the 3 T’s: Tibet, Taiwan and the Tiananmen Square crackdown.

No longer. Fast-changing geopolitical tensions, growing nationalism and the rise of social media in China have made it increasingly difficult for multinationals to navigate commerce in the Communist country. As the National Basketball Association has discovered with a tweet about the Hong Kong protests, tripwires abound. Take the “wrong” stance on one of any number of issues — Hong Kong, Taiwan, Korea, Japan, for instance — and you risk upsetting a country of 1.4 billion consumers and losing access to a hugely profitable market.

Now, multinational companies are increasingly struggling with one question: how to be apolitical in an increasingly politicized and punitive China.

“You used to know what would get everyone fired up,” said James McGregor, chairman of the greater China region for the consulting firm APCO Worldwide. “And now you don’t know. You just wake up and discover something new.”

Until recently, the issues that made China angry were fairly predictable. The German company Leica Camera created a stir this year with a promotional video featuring the “Tank Man,” the unknown person who boldly confronted a convoy of tanks during the bloody 1989 crackdown on the Tiananmen Square pro-democracy movement. (Leica says it did not commission the film.)

Around the same time, eagle-eyed Chinese internet users began calling out companies for not clearly indicating on websites, customer surveys and products that certain territories claimed by China, like Tibet and the self-governing island of Taiwan, were part of the country. Gap, Marriott, United Airlines and others were forced to make internal adjustments and, in some cases, apologize.

This summer, when antigovernment protests in Hong Kong began to heat up, such sensitivities reached new heights. And China lashed out more aggressively, in part because it was playing defense against growing global support for the demonstrators.

The N.B.A. has been in damage-control mode over the issue for days. On Friday, Daryl Morey, general manager of the Houston Rockets, posted a message on Twitter that said: “Fight for freedom, stand with Hong Kong.” Not long after, Mr. Morey’s tweet was deleted and the league quickly began damage control.

But anger still simmered. Social media platforms like WeChat and Sina Weibo were flooded with messages declaring a boycott against the N.B.A., which has a huge fan base in China. On Tuesday afternoon, CCTV, the state broadcaster, canceled plans to broadcast preseason N.B.A. games. Previously, Tencent Sports, a popular sports broadcaster, had announced that it would stop all live streaming and coverage of the Houston Rockets.

“The N.B.A. has been in cooperation with China for many years,” Geng Shuang, a spokesman for the Ministry of Foreign Affairs, said at a regular news briefing on Tuesday. “It knows clearly in its heart what to say and what to do.”

The league has also been getting flak in the United States for appearing to kowtow to China, prompting a longer, more reflective statement on Tuesday. While the N.B.A. commissioner, Adam Silver, continued to express the league’s “affinity” for China, he also said that it couldn’t regulate its employees’ speech.

For businesses, China’s national ire has tended to focus on a single issue, despite the changing targets: the country’s sovereignty.

This summer, Givenchy, Coach and Versace each apologized to China for producing T-shirts that seemed to identify Hong Kong, along with other places claimed by Beijing, as an independent country. They all stopped selling the clothes.

Navigating the potential for backlash in China’s commercial landscape now involves managing not just products, but employees and anyone else affiliated with a company.

As the pro-democracy movement took hold in Hong Kong this summer, Cathay Pacific Airways, the city’s flagship airline, came under immense pressure from Beijing to discipline employees who were sympathetic to the protesters. In a matter of days, Cathay’s chief executive was replaced and several employees, including a pilot, were fired.

On Tuesday, the American video game company Blizzard suspended a Hong Kong player and rescinded his prize money after he donned goggles and a respirator — items that have come to symbolize the protests — and called for the liberation of the city in a post-match interview. Blizzard is a subsidiary of Activision Blizzard, which is partly owned by the Chinese company Tencent.

In a statement on Tuesday, Blizzard said the player had violated a competition rule barring any act that “brings you into public disrepute, offends a portion or group of the public, or otherwise damages Blizzard image.”

“While we stand by one’s right to express individual thoughts and opinions, players and other participants that elect to participate in our e-sports competitions must abide by the official competition rules,” the company said.

The political land mines aren’t always easy to see.

The upscale jeweler Tiffany found itself at the center of a social media firestorm on Monday after posting an image of a model covering her eye with her right hand. To many Chinese internet users, the gesture evoked another symbol of the Hong Kong protests: a woman shot in the eye with a police beanbag round during a demonstration, whose image later appeared in countless posters and memes.

The photo posted by Tiffany had been taken in May, before the protests started. But it was a no-win situation for the company, which had already warned investors that it would be hurt by the drop in tourism amid the protests in Hong Kong, its fourth-largest market by sales. Mainland China is a much larger market, and the company has been rapidly expanding its presence there.

The photo “was in no way intended to be a political statement of any kind,” a spokesman for Tiffany said in an emailed statement, after the offending tweet was deleted. “We regret that it may be perceived as such, and in turn have removed the image from our digital and social media channels and will discontinue its use effective immediately.”

The backlash can go both ways.

In an effort not to run afoul of the mainland, Vans recently removed several entries from its annual sneaker design contest that alluded to the protests in Hong Kong. After that, several streetwear stores in Hong Kong pulled all Vans products from their shelves.

“Creativity is one of the keys to solving our social problems,” said Second Kill, a streetwear store in the Mong Kok district, in an Instagram post announcing its decision to stop selling Vans products. “Neither creativity nor public opinion can be erased.”

The N.B.A. on Tuesday appeared to temper its earlier apology over Mr. Morey’s tweet, seemingly to respond to criticism in both China and the United States.

For those “who question our motivation, this is about more than growing our business,” Mr. Silver, the league’s commissioner, said in a statement. He said basketball could be “an important form of people-to-people exchange that deepens ties” but noted that the two countries had different political systems.

“It is inevitable that people around the world — including from America and China — will have different viewpoints over different issues. It is not the role of the N.B.A. to adjudicate those issues,” Mr. Silver said in the statement.

“However,” he added, “the N.B.A. will not put itself in a position of regulating what players, employees and team owners say or will not say on those issues.”

Steven Lee Myers contributed reporting. Claire Fu and Zoe Mou contributed research.

Amy Qin is a China correspondent for The New York Times in Beijing covering the intersection of culture, politics and society. @amyyqin

Julie Creswell is a New York-based reporter. She has covered banks, private equity, retail and health care. She previously worked for Fortune Magazine and also wrote about debt, monetary policy and mutual funds at Dow Jones. @julie_creswell

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