Those beholden to social justice criticize Peterson for supposedly being a darling of the alt right, while the alt right criticizes Peterson for being a lightning rod that neutralizes people who would otherwise join the alt right. In other words, the left accuses him of being far right, and the far right accuses him of pushing people to the center. To the SJWs Peterson is a right-wing radical, and to the alt right he’s a cowardly centrist.
Most people engage in extensive compartmentalization. They have certain beliefs in one part of their mind, and they don’t allow those beliefs to propagate to other parts of their mind. A classic example is a person who’s able to think scientifically, but refuses to apply their scientific patterns of thought to their religious beliefs. If you try to dissect their religious beliefs with logic and show them they’re irrational, they’ll put up a wall. Your arguments will do nothing to them.