> What I mean is that freedom of speech is not the same as freedom of censoring.
This is at least not quite true of First Amendment law. The concept of "compelled speech" exists in US law, and is considered an unconstitutional violation of the First Amendment. Exactly what falls into that category (and whether the right of domain owners to censor user-provided content as they see fit is protected), I'm not sure, but freedom of speech in the US certainly does at least sometimes include the right not to speak.
Yes, the court was right to block LinkedIn's abuse of the CFAA. But the court was wrong that say that LinkedIn must show HIQ the same website as LinkedIn shows everyone else.