Free speech cutting both ways should only mean both parties are allowed to say whatever they like -- and the majority/plurality of the people decide democratically which way to go about it and who they agree with.

If an unpopular speech means you get fired, then it's not free at all. It's "be careful what you say or bad things can happen to you" -speech.

All dictatorships and all opressive regimes have such mockery of "free speech". Heck, even burning Giordano Bruno can be considered an example of "free speech" that "cuts both ways" in this logic.

(Not to mention that he didn't publicly voice an opinion in the first place. He privately backed against a bill -which was his democratic right to do- and the name of the backers was leaked).