Whenever I hear the word "Private" I immediately check my gun. There is nothing 'private' about reddit moderation, especially on a large sub like atheism (if i remember correctly, I haven't visited that cesspool since 2019). Power mods control tens of subs and cross-enforce their delusions and purity tests across them all, and reddit admins are obviously, pathetically, in league with them, always with the asymmetric tolerance and double standards. ("oh, they say 'kill all men' on female dating strategy? That's just their freedom of speech sweety. Now please remove your anti feminism post, it's harmful and ban worthy, fReEDoM oF SpEEcH dOESn'T MeAn FreeDOm FroM ConSeQuEnCEs.")
You have to stop looking at it from the ridiculous and childish private\public perspective and start looking at it in terms of right to exit and availability of alternatives. If a small, 1000 km^2, irrelevant country bans something, that's not a big problem because the residents can easily move out or otherwise subvert the ban. If a giant corporation with monopolistic control of its niche bans a thing and treats certain users unfairly, that's a much more serious violation of free speech. It's all about how easily you can get alternatives, once you reach a certain usage/alternatives ratio, you don't have the right to be "Private", you must be forced to be fair.
The public\private thing is a sort of "Stories for Children" heuristic that used to approximate the truer underlying dynamics somewhat decently, before bad faith authoritarian fan boys milked it into oblivion with cliché "Just build your own X bro" mindless slogans. The original idea being that 'public' things are usually things like states, courts, police forces and other societal structures that are usually very difficult to exit or be free of. While 'private' things are (the cliché example goes) things like gas stations or coffee shops, things you can easily exit and replace. The heuristic obviously breaks down whenever the private entity in question is $GIANT inc.