I know the Winnie the Poo one was racism mixed with "communism is when government bans things" propaganda.
Winnie the Poo is not banned in China, nor was it ever (to my knowledge). The entire meme of it came from people (mostly white racists) claiming that Xi Jinping looked like the character on sites like Reddit and 4Chan, then on the same sites they claimed the meme was banned in China and was being suppressed by Reddit's moderation (it wasn't). Thus creating an urban myth that not only was the meme of Xi photoshopped next to Winnie banned, but Winnie the Poo as a character was also banned.
This whole thing comes down to Sinophobia, and the racist desire to believe anything that's being said about China.