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.
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.
Well that's for sure. In the US I don't see the Democratic as liberal, nor the Republican party as conservative based on policies they promote.