Sure, if you use your own alternative definition of the terms, then all bets are off.

Authoritarianism is about how you’re pressured or forced to do things, and left/right is about what those things are.

I know that if we get too nuanced about all the many many dimensions of politics, then we’ll spend so all our time fighting semantics and get nothing done. But if you simplify down to a single axis then the terms lose all meaning and you likewise can’t communicate anything of meaning.