Oh, I agree. But this topic keeps coming up over and over recently.
It seems like people forget that by moving everything into the homes of Google and Facebook they agreed to these terms. You can still host content yourself. If you want free speech, do that.
It qualifies as a private company because it is, as a matter of law, a private company.
Tell me how I can refuse to bake a cake for someone because their personal views differ from mine. I dare you.
Assuming, based on your choice of example, that you're talking about the US legal context: You absolutely can refuse someone's business because of their beliefs. What you can't do is refuse someone's business because of their race, or their age, or one of small number of other protected characteristics.
I think you should be able to. But I also think that people can boycott you for doing so.