He says he's a classic British liberal, and he's vehemently opposed to totalitarianism, so it would be quite ironic if he turned out to have fascist leanings. Mind you, as I showed in my series on conservatism, all forms of conservatism reduce to social Darwinism, to regressive, primitive hostility towards modern progress (to individual liberties, civil rights, rule of law, etc).

Peterson's influence might be waning, though. Reports of recent events in his personal life embarrassed him and damaged his reputation.