It might have changed a bit after Joe Rogan's podcast but to be honest, most people outside of Canada probably have no idea who Jordan Peterson is.
He's getting a lot of support from the right, the center (e.g. Joe Rogan) and from many on the left such as Sam Harris as well. In all cases, it seems to be for free speech issues. He seems to hold a deep opposition to political extremes, though it's hard to tell what he favors other than free speech since his videos meander into mythology and literature so much.
But because of his "brave" fight against the bill, he's become a hero to alt-right and other people worried about transgendered people forcing everyone to use pronouns, and this is a lucrative market to attract. So lucrative that he now gets over $40,000 a month through Patreon alone for his classes, where he praises Carl jung, criticises post-modernism, the supposed infiltration of Marxism into culture and ideas like White Privilege and Cultural Appropriation
He's also a regularly featured on r/badphilosophy(https://www.reddit.com/r/badphilosophy/comments/64rg9i/jorda...) while there is a good discussion about him on r/AskPhilosophy(https://www.reddit.com/r/askphilosophy/comments/673zy2/dr_jo...).
You can't argue that "white privilege" hasn't infiltrated culture. An alarming amount of people have openly disparaged white people when talking to me, even though I am white myself.
If you're not white, it's almost socially acceptable to say "fuck white people" in cities like SF, NYC, and Chicago. I think it's horrible and I think Peterson is right.
I'm sure Google, CloudFlare, PayPal etc will be shutting down that blatant hate speech too.
If they want to do that, it's their right. But I will purposefully avoid companies that ban any hate speech. I've already cut ties with Google and it feels great.
https://www.youtube.com/watch?v=KnIAAkSNtqo
As mentioned, his employer's lawyers did think so. The Adversarial Model (legal system) doesn't consider that some parties come to other conclusions. It would be ill-advised to listen to "experts" that are not part of a case, taking the advice of pundits* or other unconnected parties is not compelling evidence of legal finding.
*It's primarily in the US, that the mass media promotes education pundits as corroboration in legal matters.