As someone who grew up in Russia in the 90s, I've seen it firsthand that the red/brown horseshoe is not a theory. It was often difficult to tell which one was which; even when it came to religion, our commies have all suddenly found a love for Eastern Orthodoxy.
The fallacy is that there's only one direction, so to speak. You can be left without being an authoritarian. Of course, the same goes for the right.
FWIW, I was lucky enough to be born in the US, but I've long believed that the horseshoe theory is real as well despite my somewhat flippant comments.