If I own a nightclub and it becomes a hotspot for the alt-right, who don't align with my values, and I close down that nightclub for that reason, am I censoring them? No, I'm excluding them from my privately-owned space and refusing to associate with them. Nobody's right is being infringed upon here; they're free to go to any other bar. "Whether they can host their own site" is absolutely relevant to what is and isn't censorship because all of the examples in this thread are still totally free to distribute (and even monetize) their content in public.

> am I censoring them

Yup

> Nobody's right is being infringed upon here

Of course not, who said otherwise? I just disagree wth the decision taken.

> absolutely relevant to what is and isn't censorship

You don't get to make up your own definition of the word. That someone blocks the speech is censorship, by definition, regardless of whether you can say it elsewhere and regardless of what you might want the definition of the word to be. I'm not going to condescendingly paste the definition here, but it's very clear Microsoft is engaged in censorship here.

What I’m saying is: their speech hasn’t been blocked. Microsoft is making a decision not to align with a particular demographic, not shutting them out of public discourse.

Maybe the state should provide hosting services so that the public can express itself freely without fear of being excluded.

It absolutely should, but then, I'm fundamentally in favour of more services becoming government-owned public utilities. The way this would (ideally) shake out here in Australia, though, is that given hate speech is not protected speech, the result may not be so different.

Censorship has absolutely nothing to do with the government, and I am confused as to why you think so.

Censorship is when any group at all, uses their power, any power, to attempt to silence others.

Because censors were originally Roman government officials, because the dictionary reflects this, and because censor in common usage reflects this definition.