Peterson is a weird one. He loves to play the "middle man" role and insists that he's not a right-winger, but he clearly is. Pro free-market, quotes Christian philosophy all the time, very conservative (repressive, even) about sexuality and denies climate change. Doesn't get much more right-wing than that. I think he's confused about his faith as well, he frequently contradicts himself on the issue. Political posturing disguised as self-help is an issue too, indeed. I find him disingenuous in general. Him contradicting his anti-equality of outcome stance by promoting the idea that women should settle for men that they don't find attractive so that unattractive men don't feel left out was the nail in the coffin for me in terms of taking him seriously as an intellectual.
He still is one of the relatively rational sounding voices in the new conservative movement. That's more of a testament to how many irrational people the new conservative movement has made popular, though, with Beck, Crowder, Southern, Lahren, McInnes, Yiannapoulos et al.