Why do you feel the need to put quotes around Peterson's title?
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.