There is this weird effect in American politics where each wing considers the other to be the authoritarian one.

The American right loves its military industrial complex, its police crackdowns, its bank bailouts, its manifest destiny, and so on. These are not left wing institutions in creed or membership. You could ask the same question: do you not see rightism (ingroup loyalty, moral purity, respect for authority) as naturally decaying into authoritarianism?

> There is this weird effect in American politics where each wing considers the other to be the authoritarian one.

It is weird, in a way, yes. I think, though, that when you think from each side's point of view, it makes sense that that's the case.

> The American right loves its military industrial complex, its police crackdowns, its bank bailouts, its manifest destiny, and so on. These are not left wing institutions in creed or membership.

I think you are painting with too broad a brush. There is far more nuance in what is considered "the American right" than you imply. Five minutes on the Internet and you can find people who are obviously considered "on the right" who don't agree with any of those things.

> You could ask the same question: do you not see rightism (ingroup loyalty, moral purity, respect for authority) as naturally decaying into authoritarianism?

I would ask you to more clearly define rightism, because those three things are just as prevalent on the left, if not moreso.

> You could ask the same question: do you not see rightism (ingroup loyalty, moral purity, respect for authority) as naturally decaying into authoritarianism?

Respect for authority is _by definition_ authoritarian and is completely separate from the left-right axis. As for loyalty and moral purity those seem more like talking points than actual political views.