Sure they should, but then they also have to accept the consequences of doing that. In a "free market" such as Peterson advocates for, we know the mechanism is working when it doesn't always work only in one direction. If "the market" decides that you are being a hateful ass, they don't have to tolerate that because that's a huge part of what it means to live in a free society. That's the free market at work. The fact that you (and I must say, too many other people) don't seem to understand this distinction is pretty troubling, but from my perspective, I'm much more of an actual free speech advocate than you are, because I acknowledge that part of what real free speech truly means.
For example, your employer has huge wide latitude to compel you or forbid you to do or say all sorts of things because (at least in the US) free speech rights only apply to the government not being able to curtail your speech - except for all the ways that they absolutely, legally can. If you and I meet on the street, I can't have you fired or arrested for not addressing me respectfully, but in a government, school or work situation, it is absolutely appropriate for there to be rules of conduct that everyone has to abide by - particularly for such things as professors treating their students with basic humanity and respect. You are not honestly saying that you think it's fine if Peterson or someone else wanted to call their female students "sugar tits" or their Black students the "N" word, because people "ought to be able to think and say what they want to"? Are you? Because that would be both chaotic and insane, and the breakdown of a civil society.
I read something recently where the author was moaning that the Canadian Psychological Association (or some such professional body) wanted to require Peterson to take some sensitivity coaching and how that was such a blight on his free speech. On the contrary, if Peterson wants to remain a member in good standing, he has to comply with their rules. I'm sure he won't, and that's his prerogative, but that's actual free speech at work. He has no human right to be a member of that professional body, and although he is free to say what he wishes, he is not free to do both - belong to that organization and say objectionable things. I'm not sure why that is such a difficult concept?
