This is actually an decent question; I tend to favor view that platforms should have less room to censor in scale with their size. The idea being that a tiny forum can censor at will because its impact is minimal, whereas YouTube shouldn't be allowed to censor legal material, because forums are a dime a dozen, but YouTube is a monopoly, so if they decide they don't like you then you effectively have no voice. This is the same problem as malls and the like have; privatization of public space doesn't make the space not public.
Also, I would oppose censorship in your particular examples. I would think that it is your right to publish in the NYT under the same terms as anyone else (i.e., be interesting or have money), to top HN (if upvoted), or to speak in my home (if invited). And if the NYT blacklisted someone speaking on corrupt reporting, if HN blocked stories because they were right-leaning, or an acquaintance refused to talk to me because they disagree with my politics, I would be rightly upset at them.