Well you forgot about the fact that because they are classified as a media source, and the first amendment also gives us the right to freedom of the press/media, they also have to follow the constitution since it's a federal documentation and law. Which means they can't censor your speech. Facebook got in trouble for the exact same thing.

Except the fact that even they have to abide by any federal laws such as the constitution.

If you are an American citizen, take them to court as it's a violation of your first amendment right to freedom of speech.