> Funny how this argument is only put forward for cases in which the author agrees with the censorship.

Not really. I've frequently seen the argument made that particular censorship is within the legitimate purview of a private actor, while still being disapproved by the speaker.

> If facebook tomorrow banned all LGBT content I have a feeling "it's a private company" would not be an acceptable defense for anyone currently using it.

Facebook absolutely has the right to censor all LGBT content, and them doing so is not a cause for government intervention.

Facebook also absolutely should not censor all LGBT content, and I would condemn them and cease use of the platform if they did.