Pussy Riot was arrested for making a loud and noisy spectacle in a church that offended the sensibilities of most of the church goers in attendance. Pussy Riot called that a "prayer" if I recall correctly, but most of the people in the church called it an obscenity. Unfortunately, Russia never had a law against offending the sensibilities of an entire church full of people, so they got charged with hooliganism instead. I think the Russian courts simply wanted to let Pussy Riot know when enough was enough.

And, I'm not sure I'd call China a "communist" country anymore. They were communist for a long time, but now they seem to be just as capitalistic as their arch enemy; Taiwan. There is an unspoken social contract in China. If the government makes you wealthier and makes your life easier, you don't criticize the government. Both sides seem to be holding up their side of that agreement, so what we have is 1.6 or so billion people all wanting to buy their own condos and cars, living under a supposedly "Communist" government that now allows private ownership of property. It's perhaps Communism wearing a completely new wardrobe.