The First Amendment applies to the government, not civil society. If E!, a private cable TV network, doesn't want to broadcast someone's comments, they don't have to. It really is that simple; the US Constitution has nothing whatsoever to do with it.
That said, if you disagree with their decision, let them know. It's stupid, and they should be punished in the market for it. But along the way, please don't invoke the Constitution. It's got nothing to do with anything here.


