On websites across the internet, this happens. Even here apparently. Facebook.com does it. Meetme.org does it. Twitter.com does it. Anywhere a Moderator dislikes your opinion, they remove, ban, block, or terminate you and your posts. This is illegal and the equivalent of organized crime. Many times has it happened to me on Facebook and Meetme, for I speak my opinion on issues. And I know a conscious individual does it, as the next posts I enter are confronting the entity stifling them: and they reciprocate often, the censorship stops. But starts again inevitably, and sometimes it doesn't stop when confronting the abusive Administrators. No amount of emails stops this. The only thing that does is Civil and Criminal penalties or reprimand. They censor what they don't like. It's Orwellian, and it must stop.
Facebook's "community standards" are applied in an absurdly biased manner. Their “community standards” are apparently interpreted through the agenda of Christophobic pansexuality, to remove expressions of Christian values, at the behest of the Christophobic homofacists through the Facebook reporting process, while ignoring egregiously insulting posts of the same activists targeting Christians.
I think that it is safe to say that most social media sites that are controlled by a moderator are in fact subject to that persons' personal beliefs. While it would be nice to think that everyone could remain perfectly neutral, it is not a very realistic expectation to think.
It's not just moderator's but the majority view. Sodahead (Ku Klux Klan) is a perfect example of a site still stuck in Jim Crow mentality. The shame of it is though is not that they disagree with my views (they're bigoted though), it's mostly that they kick off people who mind their business only for not having the right views. Now I'll never be able to find a site that I could make friends.
I have yet to see any kind of concrete evidence that would show me that social media sites go around and systematically censor anything that is on there that they disagree with. While any moderator is subject to being influenced by their own thoughts, it doesn't appear to be a big problem.
To my left you see somebody saying yes and citing valid reasons for doing so, but I have to give this an overall no because of how the question is presented. Social media sites do not by default silence you because they don't like you. I've been a member of a board that the owner tolerates me at best and I can say whatever the heck I feel like. Some social media sites shut you down if they don't like what you're saying, some don't. The category can't be all grouped in one basket or the other.