Youtube isn't saying that no one has the right to say ridiculous nonsense, they are saying that they can't use their platform and infrastructure to do so.

Well, on one hand, there's a group's right to say what they like, and on the other, there's the discussion of what a corporate platform should host for free, what they can remove, what they ought to remove, what they're required by law to remove, and whether/how monopoly status changes any of that. Those are thorny and nuanced questions that catchphrases are no use in solving.

Also, we were already off topic when you mentioned censorship, so Nazis aren't that much further a digression. I think the real topic here is that Youtube can never possibly support a moderation team proportionate to its size while still offering free uploads, so it's limping along with garbage moderation that often has disastrous effects.