"The Fact Checkers (TM)(R)"... what are they in this case? They are employees working at the behest of the owner of the property of which you are a guest.
Should a company the size of Facebook get Section 230 protection? Probably not. Should government officials be allowed to use social media sites for official business? I don't think so. Should campaign finance laws be strengthened and ad spends on social media sites subject to much more sunshine? Sure. And should meta be broken up? Yeah.
I'm not here to defend Facebook, and I think the interventions I would propose to deal with the Facebook Problem are probably far more damaging to Facebook the company than "no more moderation".
But compelling speech is also a violation of free speech. If you demanded that I post your article on my personal homepage, I'd politely tell you to bugger off. And if you insisted that I should have to do so, I'd consider you an enemy of free speech.
Apparently you don't feel the same way about FB.
But where does that line get drawn?
And what, exactly, is FB allowed/not allowed to censor (and don't be glib, the answer "nothing" is functionally equivalent to "make FB 4chan" and I think you'll find fewer than 1% of the population that is radical enough to think that would improve things)?
Who decides?
We don't have good answers to those questions. They're fundamentally questions about who gets enormous amounts of political/economic power. Power corrupts. But even if we did have good answers to these impossible zero-sum questions, we still wouldn't really have a decent solution to the underlying problem.
The problem with platforms like FB isn't primarily caused by the content of any particular speech and so can't be solved by censorship of FB users or of FB itself. The wariness about FB is reasonable, but the instinct to solve the problem by censoring FB itself is all wrong. It grounds out a massive political struggle and doesn't even solve the underlying problem.