How bad is online harassment?
[reason.com]
"You're a poopy head!" "I'm telling the teacher!"
There aren't many realistic threats of violence, and everything else basically boils down to people taking insults from strangers way too seriously.
Incidentally though, I think it's possible that the apparent bias in censorship may at least partly be due to ideology. The more authoritarian left is more likely to report something offensive than those who favor personal responsibility more and therefore will respond themselves rather than requesting censorship. Of course it's also highly probable that the openly leftist censors favor leftists, but that's not the whole story.
You're probably right about that pertaining to ideology.