Everything you just said is essentially untrue when it comes to government censorship of speech in the US. Hate speech is certainly protected by the first amendment, with only a few narrow exceptions. Personally addressed, face-to-face insults, if deemed likely to start an imminent fight is not constitutionally protected.
(This is sometimes called the "fighting words" exception, and it's much narrower than you might think. The law is quite clear that just because the words might yield a violent reaction, they're still protected. Cantwell v. Connecticut involved anti-Catholic "hate speech", as we'd now term it, expressed in public in a neighbourhood that was 90% Catholic, enraged many listeners, and almost started some violence. Still protected.)
> You can still have freedom of speech while implementing moderation to make sure that hate speech, bigotry and fake news don't spread
Only if done, as here, by private organisations. Regulating bigotry on message boards is the precise thing type of things that the first amendment prevents.
There is no hate speech exception in the constitution. Hate speech is generally an example of what is most protected.