It's usually non-Chinese people that use the Pooh caricature (huh, wonder why?), and again, that doesn't change that the overwhelming majority of Chinese citizens do support their government. Check the study I linked, public opinion is most closely linked to real material well-being, like Upward Mobility:

There is a good deal of criticism for the CPC, a lot of it is coming from younger generations that want to accelerate the progression of Socialism. This isn't censored, but what is usually censored is when right-wing, Western media tries to propagandize. In reality, things are improving, so more Chinese citizens are satisfied, and take an active role in building up their country.