While the army in Avatar is undoubtedly American, the idea of people siding with an indigenous population against an imperialistic force is something that China was not comfortable with. That's why shortly after the release of the movie in China, the authorities decided the movie could only be shown in 3D. Since there are very few 3D theaters in China, the move was effectively a ban on the film.
Read the reasoning behind the other bans at Oddee. Link