I think a massive problem with his popularity is that much of the deeper underlying context of his beliefs (i.e. dense clinical psychology) gets totally passed over by people on the left AND the right (or wherever else) who want him to be something more than he is. The above poster is absolutely right in saying typical conservatives are unlikely to bother reading his books properly and so likely get most of their ideas about him from edited youtube clips which makes it a lot easier to feel as though he is dog whistling or waving a flag for right wing politics. The exact same thing is true of the 'left wing' contingent who are convinced he is racist, transphobic, sexist etc from the same reduced, surface engagement with anything he may have written or spoken about in depth. Peterson says and does plenty of things that I think are stupid and badly argued, but he still comes from a field that would offer a lot to the current state of political and social discourse if people were prepared to interrogate their thinking a bit more than simply picking a side. It seems people are very quick to forget the PUBLIC part of public figure. When people are increasingly convinced of what they believe before engaging with the topics at hand then it doesn't matter who this year's big topic is or what they have to say. And that's the way of it regardless of where you find yourself within the spent and meaningless spectrum of 'left or right', 'liberal or conservative' we still find ourselves banging our heads against.
All this is, of course, why the above poster is exactly right in saying nobody will give a fuck about him in a few years and why, despite whatever he might be trying to achieve, he has now got himself caught in a game where he can say whatever he wants but people will only hear the parts of it that they want to. A game he probably should have known better than to have engaged with in the first place given that his whole bag and the context for most of what he says and thinks is an understanding of the psychology that gets us all playing.