The misconception is that freedom of speech means anything other than freedom from prosecution by the state for your speech. It does not mean you are entitled to a platform, it does not mean you cannot be shouted down, and it does not mean private entities cannot (or even should not) censor your speech.

It’s important to keep unpopular speech legally protected. It’s not at all important to ensure it has a robust platform. For example, Nazis should not be arrested for saying Nazi things; but they should absolutely be deplatformed, socially shunned, and have a blind eye cast when they get punched in the mouth for saying Nazi things in public.