While individuals and private entities are not obligated to follow that law because it is direct at the government people can rightly complain that it is in bad taste when they stray too far from holding themselves to the same standard.
A private entity banning confederate flags and nazi symbols in avatars is palatable enough on its own. But it is decently close to having to censor those sorts of things in legitimate historical contexts. See for example all the genuinely historically centered youtube channels that have to censor those symbols because otherwise the algo will bury them. I think we can all agree that that latter case is not ok and is the kind of censorship that should be complained about. Considering how many historically themed video games there are out there and how strongly people believe in free speech it's understandable why more than a few people do not like this move by Twitch.
When machine translation gets so good as to be transparent, correct, and effortlessly ubiquitous, we'll probably see more cross-cultural communication. And along with it, a bunch of additional clashes, new taboos, and additional reduction in the range of acceptable expression. I probably say things that someone halfway across the planet thinks are abhorrent all the time, and I only get away with it because we're not interacting yet.
This mostly changed due to 'corporate personhood', the idea that corporations should have the same rights as people.
This article goes in to a lot of how this has lead to corporate abuses of power:
https://repository.uchastings.edu/hastings_law_journal/vol41...
This one's an easier read, but basically an editorial on the one above:
https://reclaimdemocracy.org/corporate-accountability-histor...
You have a right to free speech. You don’t have a right to force everyone to listen. What a fucking awful world that would be.
What would the side effects be of not being able to remove people from your store because they're behaving in a way you don't like? What if YouTube could not, legally, remove content that was "abusive" or "hateful"?
(Again, not saying I think this is how things should be, just trying to entertain the idea a bit.)
The discussion about what is and what is not reasonable censorship should not be limited to constitution and its meaning.