Just to flip this, do you have any sources that horseshoe theory is a real thing? That's the funny thing about language, someone put Theory in the name and now people think it's a real thing.
To save you the trouble, it hasn't held up under academic study. Plenty of info on Wikipedia about it.
America has two authoritarian right-wing parties to pick from. One is less right wing than the other, but they're still both to the right of the major right wing party in my country (New Zealand)