Censorship is a loser move
Censorship is running rampant, but I've seen people argue that it's not censorship unless government is doing it. That's not correct. Censorship doesn't only refer to government action.
While the First Amendment prohibition of censorship only applies to government organs, because those are the only ones who can use legislation to prevent someone from expressing an opinion (or telling an inconvenient fact) or hearing the same, it is still censorship if I prevent you from speaking or being heard. I'm not individually obligated to promote or "host" your message, but if I take action to prevent it from getting to those who want to hear it, I'm censoring just the same as if I banned you from expressing it.
If I deleted comments from my blog which expressed an opinion I didn't like, it would be within my rights... and it would still be censorship. I wouldn't feel right about doing it because, to me, censorship is never ethical, even when you have the right to do it.
The first definition of "censor" is "an official" who suppresses [things] deemed objectionable on moral, political, military, or other grounds. But the second expands that to be anyone who does something similar. That encompasses employees of Twitter, Google, Facebook, and all other quasi-governmental, pseudo-private, institutions.
As I have pointed out on the topic of "private prisons", if it's wrong to do something, it doesn't magically become right just because it's not being done by a direct government employee. It's wrong if done by a corporation or by a private company or by an individual. Murder isn't wrong only when committed by a cop, and censorship isn't wrong only when committed by a government censor. Even though the First Amendment only applies to the direct government employee.
Interestingly, just after I wrote this I ran into something very similar linked over at Claire's blog. I suggest you read that one, too.