In the political alignment chart, authoritarianism falls on y axis, whereas left/right is x axis. This explains why you find people from both sides supporting it. They're essentially the same side as far as this topic is concerned.
I've often been annoyed by the left/right divide being spoken about as linear. Its always felt more circular to me, you go far enough to the led or the right and its hard to tell the two sides apart.
Authoritarianism as a second axis is interesting, though I don't know what the opposite would be. Communism, the actual idea with effectively no one in charge? If so, in practice those extremes seem to end up in the same place, one or a few people in charge of everyone else with a very tight grip on power.
I agree that extremists of all stripes are troublesome for various reasons. The sibling comment by `odo1242` already answers the y-axis question. I want to note that these are idealizations, and may not perfectly map to the parties labeling themselves as such.
In the political compass, the two axes are liberal/conservative and authoritarian/libertarian. So it would be “libertarian”. This includes philosophies like anarcho-capitalism (bottom right) as well.
