I think the big difference between private and public is that the public authority uses force against the property of others to exclude speech, supposedly deemed as disgusting to a particular group, but you have to recognize as history shows that it will be abused to limit legitimate political speech.

Private forums like Hacker News in no way infringe on the rights of others, by using their own property (web site) in a way they deem fit.

I agree that HN can operate how it wishes.

I'm not sure that barring disgusting speech is "necessary," if only because "necessary" can be such a loaded word.

reddit, for example, seems to have a principle of free speech, where there only a very specific things you are not allowed to say board-wide. So there is a fair amount of disgusting speech there. It seems to work for them -- although I have been slowly disengaging from it over the past year or two, and maybe that's part of the reason.

Don't some individual subreddits moderate fairly heavily? And the upvoting/downvoting also has the effect of hiding disliked speech.

Yes, they do, and the admins support lots of freedom and experimentation for the subreddit moderation policies. (Although there are "default" subreddits that are a little weird.)

The sitewide bans, to my recollection, are of only two things (besides that which is illegal): sexualized pictures of children, and doxxing.

Right, there's a difference between tolerance and embedding it in your community's culture.