Extending this body of law to, say, Facebook would have problems, of course. But I don't think it's so clear that all sensible adults know that censorship is only something the government does, and are happy letting any corporate behavior, no matter how extreme, pass without scrutiny.
The larger point I was trying to make still stands. I think.
Specifically, that speech in a private context is not subject to the same amount of regulations as speech in a public context (with the incorrect interference that only the govt can restrict speech in a public context). Marsh v. Alabama specifically argues that the sidewalk in a company town is equivalent to a public space. (And I think that does hold interesting questions for large web sites).
But free speech rules still apply to a lesser extent on both commercial and private properties. The idea that "censorship for comfort" in general is bad is misguided.
(In the context of above lawsuit, I'd love to hear a lawyer expand on if content restrictions qualify as restricting speech in a semi-public content, or if they qualify as making the space less public - i.e. are they barriers to access, or to speech?)
I think the point I have in mind is that there are less restrictions on speech as the venue becomes more private, and this is for good reasons, large websites as a platform for mass conversation are relatively new, and come with their own benefits and drawbacks when they choose to restrict speech. And because these trade-offs are new, the debate should be about these pros and cons, rather than flat statements that censorship is bad, or that private companies can do whatever they want, no matter how severe.
It should be a policy debate. The CA constitution probably doesn't apply, but the legislature can intervene anyway, and I don't think an argument that says "these platforms are important enough to modern-day communication that they should do so in some manner" is completely insane.
For example if a newspaper publishes inaccurate information about a person, that person has the right to publish a correction[1] explaining their point of view on the subject; and the newspaper is forced by law to publish the correction in the same venue and same prominence. This is considered quite sensible to us.
And you'll note that even the ACLU is perfectly fine with the government restricting speech in some well-defined circumstances[1].
[1] Visible if you see the full text of the blog post you linked: http://www.nybooks.com/articles/2017/09/28/why-we-must-still...