Notice that while their economic goals are at complete odds with one another, they are both authoritarians.

You’re thinking of the political compass there, which has two axes, one being the economic one (left/right) and the other being the Authoritarian (top) vs Libertarian (bottom) axis.

But the left/right most people use is a one-dimensional system which puts everything on that one axis. It’s based on how the French parliament used to be set up between the radical left and the aristocratic right.

The point being, the two left/right axes aren’t equivalent. I personally also think in the political compass, that’s the system we learnt in school, so I’m unclear on what falls where on the basic left/right axis. But Wikipedia has this to say:

While communism and socialism are usually regarded internationally as being on the left, conservatism and reactionism are generally regarded as being on the right.[1] Liberalism can mean different things in different contexts, being sometimes on the left (social liberalism) and other times on the right (conservative liberalism or classical liberalism). Those with an intermediate outlook are sometimes classified as centrists.