[theorique]

That is not trampling the First Amendment.

Correct - that only refers to prohibition of government censorship.

I suspect that Facebook wants to keep things "nice" (for some value of "nice") so that the advertisers won't get spooked away and they can continue on their trajectory of world domination.

The trouble is that not every user, advertiser, or activist group agrees on what is "nice", or at least "permissible".