> Twitter has the absolute right in the free market to moderate as they see fit when free speech only protects from governmental actions

You confuse free-speech-the-legal-concept (which yes mostly deals with governmental actions' with free-speech-the-principle. You treat the law as if it was equivalent to the moral norm, and that's just not the case.

Yes, twitter is legally allowed to moderate as they see fit. But just because what they do is legal does not mean it is right.