But I've made an exception for Peterson. He's not as super left wing as much university staff, sure, but to call him extreme right is very far fetched.
My impression, if this means anything to you, is that his political opinion fits well with that of centrist Christian Democrat parties in Europe (eg Merkel's CDU). That makes him more conservative than me, but because he's also totally brilliant, I don't mind.
I don't know why the alt right likes him, but my guess is that he's a great speaker who presents something like a very moderate version of alt right opinion.
I guess the most extreme thing he did, that he's somewhat infamous for, is refusing to use different singular personal pronouns than "he" and "she". While I think that he was an ass about that, to call someone far right for not wanting to say "ze" in a classroom is a few bridges to far for me.
EDIT: I got 4 downvotes already but really tried to make a balanced argument. Maybe I missed some of his "oeuvre" that would change my mind, maybe I'm outright wrong somewhere? Would appreciate someone pointing it out.