Horseshoe theory can't tell the difference between actual similarities, contingent effects of the existing political spectrum (contrarian personality types, say, or people who see the problems with the existing ideology but don't have answers and end up jumping back and forth between alternatives), and absence of traits unique to the ideology of the observer.

It's also a useful propaganda tool:

...the postwar American development of a conceptual vocabulary - “totalitarianism”, “authoritarianism”, “statism”, “central planning”, horseshoe theory, “human rights” - by which communism and fascism were positioned as varieties of a broader unitary category and America assured itself that it had always been at war with Eurasia.

If the public/private divide as thought by classical liberalism is unique to classical liberalism, of course things will look like a horseshoe: as you go further from classical liberalism, you see that the importance of/adherence to the classical liberal public/private divide falls away -- which must mean everything that isn't classical liberalism is the same, right? No.

I'm not sure where you're getting the stuff about NRs favoring government regulation in private contracts and hiring practices. Or the "accused of"/"are, more or less overtly..." distinction: many SJWs show overt hatred (resentment weakly disguised as contempt, as resentment usually is), and if anything, resentment-based hatreds ought to be treated as more worrisome than contempt-based hatreds, since most genocides are committed out of resentment, and most of the exceptions (like those of the British Empire*) are motivated by a drive for lebensraum, which doesn't really apply here.

• Obligatory footnote to avoid connotationally reinforcing a common misconception: the vast majority of the killing in the Americas was done by Old World diseases and was inevitable given contact before the development of modern epidemic control, and the smallpox blankets are generally considered to be a myth. I'm not sure what the statistics look like for Australia.