Firstly, I don't think I ever made a slippery slope argument. That seems to be something you've read into my comments somehow.
Secondly, any legal distinction is established via a multi-part test. As a first pass, I would ask:
1. Is the site open and particularly, targeted to the general public?
2. Does the site enjoy widespread use by the general public?
3. Is the site intended to foster open discussion on any topic? For instance, the public itself drives most conversation on the platform.
This isn't necessarily exhaustive, just a first pass. HN is targeted at a technical audience (although its open to anyone), it's typically used only by this subset of the general public, and its content is narrowly focused on technical subject matter, so it would fail two parts of this test.
Facebook definitely passes all three qualifications, Twitter doesn't have as widespread use by the general public but it continues to grow.
> What about all those shadow banned users, are they entitled to their free speech on any website that allows comments?
Shadow banning seems like a poor idea. Terms of service that encourage civil discussion are perfectly fine, and violators should get an explicit and public timeout, never a ban. I've toyed with the idea that repeat offences trigger exponentially increasing timeouts.
Judging violations of ToS should be a transparent process. Something like jury duty as a term of using a service also seems like it might be a workable idea. Corporations have their own motives for censorship, primarily profit motives to draw in advertisers, and so they have incentives to bury anything even remotely controversial and are not incentivized to evaluate anything "fairly".