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.
Good thing I didn't say that.
Too bad you missed when I called both "bad"
Two things can both be indefensible, and yet still one is preferable. Although you lead with "and", you seem to be suggesting that this isn't the case, which is a wild position that doesn't hold up to even that barest of scrutiny.