The recent remake of "Red Dawn" was initially conceived as a paranoid thriller about an invasion of the American homeland by Chinese military forces. But in post-production, every reference to China -- dialogue, names, uniforms, flags -- was replaced with a reference to North Korea out of fear of upsetting Chinese censors. Ironically, the fact that North Korea is so economically weak enabled the filmmakers to cast them as such physically powerful villains. Presumably if North Korea suddenly decided to start permitting American films into the country, the producers would have had to recast the bad guys again (to, I don't know, mad invaders from the Maldives or something).
As Vadim Rizov's fine article for Film.com makes clear, when it comes to the international box office these days, China's the country with the true power. When movies aren't cutting out potentially objectionable material for the Chinese market, they're cutting in additional scenes featuring Chinese actors and storylines. Why? Rizov's primer on the subject:
"China's ever-increasing role in the decisions Hollywood makes have been an urgent topic of discussion for years now; various projections all conclude the country should be the second-biggest market in the world by the end of this decade. Consider 'Iron Man 3:' as of pretty much right this second, China has contributed 10% of the film's nearly $1.2 billion worldwide gross, one reason why Marvel was ready to hire a consulting agency to help it gain official approval. Like two recent releases -- '21 & Over' and 'Looper' -- the strategy was to create China-only footage that would win the authorities' approval to make it one of the 34 foreign films released in the country this year. That strict quota can be evaded by making an official co-production, but the rules for that are stringent: 30% of the production funds have to come from China, 30% of cast and/or crew must be Chinese, and the film must meet the nebulous standard of reflecting Chinese values and themes. (The major example so far being the 2010 remake of 'The Karate Kid,' though the final product was still recut to meet the censors' standards.)"
"Iron Man 3"'s additions, involving a pair of Chinese surgeons (played by Fan Bingbing and Wang Xueqi) who operate on Tony Stark's robo-heart, existed only to help the film gain traction in the Chinese market; by all accounts, you gained little by watching them and you lost nothing by missing them. The really interesting part of Rizov's piece is when he describes other movies that have made far more substantial content changes to appease Chinese officials. Take, for example, the movie "21 & Over," about a bunch of American buddies who celebrate their pal Jeff's (Justin Chon) 21st birthday with a wild night of partying. Or at least that's what American audiences saw...
"The point of the American version is that Jeff realizes he doesn’t want to be a doctor and stands up to his traditionalist dad, but in the Chinese cut he’s a Chinese transfer student who wakes up, realizes how terrible American lack of discipline is, and returns home to become a diligent doctor for the homeland. This, the 'Los Angeles Times' noted, gives the film the special distinction of not only giving 'the film a different feel but in fact also actively casting the U.S. in a bad light.'"
That's more than adding scenes; that's adding a wholly different theme than the original film contained.
Generally, these China-friendly cuts have not been well-received (that Kotaku article says many Chinese moviegoers actually "hated" the scenes with Fan and Wang). In an free marketplace, that would probably kill the push towards pandering scenes in a matter of months. But the Chinese market is closed, and carefully controlled by government censors. The added scenes might piss off audiences, but if they please the censors, then Hollywood's going to keep making them for a long time to come.