I don't think left-wing or right-wing makes sense here, it's small-l liberalism versus authoritarianism. In particular a lot of authoritarians are ideologically shallow and happy to adopt leftist/rightist beliefs opportunistically.
Which is likely how most of the USA splits politically as well: libertarian (classic liberal) vs. authoritarian. The Republican/Democrat split overlaps to some degree with this, but those axes are usually split by a handful of hot-button issues.
