The discussion here is about censorship. Infringing the first amendment is censorship, but the converse isn't true. Plenty of things are censorship without infringing on the first amendment.
As an example, Bezos hypothetically preventing his newspaper from publishing negative stories about him is censorship. He is censoring his editors in this hypothetical.
As another example, if Bezos says "everyone who calls me a stupid-head will get kicked of AWS", that would be an attack on free-speech.
My point is that unless something violates the first amendment, I’m ok with it. If Bezos kicks people he doesn’t like off of AWS, I’m ok with it. It’s not a public space. The owner of the private space makes the rules. Just like I can kick people out of my house for similar reasons.
Don’t like it? Host it yourself. If the government tries to censor your self hosted content, then I’ll get up in arms.
Fair enough, not sure that is the point of the XKCD comic though. I believe the point of that comic was "banning racists from twitter is not a first-amendment issue".
I believe the public discourse is affected by much more than the government. To keep that public discourse free enough is important for democracy to function. Hence I fear more than just government trying to repress certain forms of speech.
That doesn't mean I want to legally ban all such repression. I also don't believe democracy would be better off if actual neo-nazi's were unbanned on twitter. Instead, I think its important we keep track of repression of free-speech, discuss what people consider acceptable, and reach some rough concensus. Based on this, we can then develop either alternative platforms, or make some well-thought out new laws.