I mean, there's clearly something to the idea that free speech rights are implicated in Twitter banning Alex Jones. The retort that free speech is only about protection from the government is just plain silly. It's libertarian nonsense. I'm a liberal, not a libertarian -- I think that exercises of private power can also create injustice. That's why stuff like the '64 Civil Rights Act is so important, since sometimes abuses of private power can be such a problem that they justify government action.
I think almost everyone here would agree that it's a big problem when corporations punish attempts to unionize. Obviously it'd be a huge problem if corporations were cooperating to identify people organizing more broadly for political change the corporations don't like and then making their lives hell. But what is the actual wrong here? It seems to me that it's basically a free speech or free association thing. It's wrong for your boss to try to coerce you into not organizing a union with your fellow employees, because you have a moral right to form a union. It'd be wrong for the people who control most of the country's wealth to use their economic power to punish your attempts to change policies that are benefiting them, because you have a moral right to try to get those policies changed. These aren't violations of the first amendment, but they're infringements of a moral right to actually-not-just-technically free speech.
But as with anything about moral-but-not-legal rights, adjudicating individual cases can get messy. No one really believes in an absolute right to free speech, where it's wrong to ever do anything to disincentivize bad speech. We can and should make distinctions about power imbalances and kinds of speech. And this is where I think Maher and friends are actually going wrong. It would be wrong for Twitter to ban someone just for having unpopular political opinions. But that's not Alex Jones. He slanders people constantly and defrauds his audience. he incites harassment. The justification here isn't "we don't like your speech", it's "your speech is evil". Obviously any time we have to make a judgment like that we need to be sensitive to the possibility that we're only deeming the speech to have crossed a line because that justifies us in going after the speaker, and so we should be err on the side of caution when we draw the line, but Alex Jones is so far from anywhere the line could plausibly be that it's not a tough call. And Alex Jones isn't just anyone, either. He's not being silenced. He's still going to have a massive audience for his crap -- he's not reliant on Twitter for participating in political discourse the way that some other people might be. So Twitter isn't actually doing much to harm him, and his speech should be silenced, so we shouldn't be worried about a lack of respect for substantive free speech in this case. But I don't you can legitimately (and I don't think it's persuasive to) dismiss the idea that there's a worry about free speech here because there just couldn't possibly be a reasonable free speech worry about Twitter banning anyone.