I definitely get the "my company - my rules" POV. The First Amendment doesn't apply to private spaces.
Then again, I'm not convinced that moderators ought to have the power to control what sorts of ideas are interrogated publicly (e.g. in the company of strangers). It's particularly problematic when the social climate at the companies that control these platforms is synonymous with the Progressive echochamber, but it's also hard to imagine any body that would be qualified to police ideas.
One of the worst things to happen this decade is the rise of social echochambers, where groups of people intellectually isolate themselves amongst likeminded people, writing-off dissenters as evil strawmen. The groupthink in these echochambers is nudged further to the extremes by the loudmouthed activists who control what ideas people are comfortable expressing. Large groups isolating themselves in these constantly drifting echochambers leads to the problems we saw this week in Washington. I fear making the platforms synonymous with these echochambers will only make this problem worse.
Anonymity and free expression have historically been some of the best qualities of the Internet. Anyone can say - and think - anything, and share those thoughts with everyone. That's always included snark, parody, and similar absurdities. People don't always mean what they say - they often might not even know _if_ they mean what they say.
Those same qualities make it particularly vulnerable to misinformation and conspiracy theories.
Figuring out how to help people understand what's likely to be true without censoring the kinds of ideas people can openly express is one of the great challenges of our time. I really hope we solve it.