ISPs are considered common carriers, which Net Neutrality addresses:

https://en.wikipedia.org/wiki/Common_carrier#Telecommunicati...

I haven't seen this same argument made for websites in particular. If you have good references for that, please do share!

btw, did you create an account just to make this comment? If so, why? It doesn't seem too controversial.

No real reason for the account creation, boredom mostly (I lurk).

And I think that's the point. ISPs are precedent to show that a company being private isn't of itself a good enough reason to let it censor people. Google and Facebook are big enough that I think they should be considered public fora for speech. Hence the term "Gatekeeper" in the OP.

I understand what you're saying, but I know that I'm not qualified to give an informed opinion. So I'd prefer to see a more legitimate source than speculation on HN :)

Just riffing here, but would it be fair to require Amazon to sell any product I want to make available?

If the UN declared your product a Human Right, seems possible.