Earlier quoted context omitted.
So far, I haven’t really seen it outside campuses, but there is a strong push to have private companies deplatform people, and government action is always a tool in the toolchest that people might invoke. As to your second point, FIRE tends to advocate for free speech on campus generally, including private schools. A lot of the right-wing attempts at suppressing speech happen at places like private religious schools…
But private companies deplatforming people is exactly the thing you were speaking approvingly of earlier; that's simple freedom of association, articulated through commercial pressure.
I think private companies doing that based on commercial pressure is fine. I don’t trust, however, that it will stay that way. Many of the same people who approve of those efforts also see government intervention is a key tool to achieve social policy. (Which is also something I don’t necessarily oppose.) I just worried about what could happen when those two lines of thinking collide.
Deplatforming hate speech based on commercial pressure is a temporary alliance between progressives and liberalitarians. It wouldn’t be the first time, however, where such alliances have broken down as progressives pushed harder.