Can someone living in the US tell me how this could be legal? Surely it's not?
There is no "right" to free speech in the US between 2 non government entities.
This would be illegal if a publicly owned entity had this policy (say a historic library or a public garden)....
It's stupid and probably not enforceable, but its a civil court case.
This contract holds you responsible for others' behavior, which is less well established.
There's the First Amendment and then there's free speech.