> But there is considerable extralegal hate speech regulation. Your face will be plastered all over social media and you will get "cancelled" and lose your career

That's a pretty convoluted way to say "people in the US don't tolerate assholes".

> and no "free speech" laws will protect you from that

You have a right to speak freely without the government stopping you. You have no right to have people listen to you. In fact the same guarantee that you have for speech also enshrines free assembly.

So everyone who disagrees with your bullshit is free to ignore you and convince others to ignore you. They're also free to boot you off or out of their property.

Important distinction: the government is allowed to do violence to people legally (during law enforcement). Private people generally are not.

This means that if you have free speech, you can't immediately suffer legal violence for saying things.

You may, of course, suffer other things, but it won't be legal violence.