No. It's reasonable to fire someone who berates other employees. It's reasonable to kick patrons out of your store if they harass women. It's reasonable to kick out a belligerent customer.
But Twitter is none of these things. Twitter is a platform for discourse.
If they want to be totally hands off, they can do that. But if they want to set a tone for how people use their service, they can do that too.
Reddit is a platform for discourse too, and they've decided to evict certain communities from their platform because they don't match Reddit's goals and values. HN is a platform for discourse and there is a reputation system that controls how people interact with it. Facebook is another platform where users can decide who they interact with, and how.
Yes, they can. I'm just going to repost my canned response now:
>The government supports free speech because it's important and a Good Thing. Just because private companies aren't required to do the same doesn't make it any less important and a Good Thing.
Is it a good thing if someone at your job shouts racial epithets at you all day? Should woman have to tolerate being jeered and catcalled at every private business they patronize? Should a restaurant turn a blind eye to a belligerent customer that curses at the wait staff and everyone in ear shot?
Of course not. A private business has a vested interest in creating an environment where customers feel welcome. They could also choose to do nothing and let the chips fall where they may, but if enough bad actors make things bad for everyone else, that business will fail.
You have a right to not face retaliation from the government for speaking your mind. It doesn't mean everyone else has to accommodate whatever it is you have to say.