Realistically the left/right spectrum is orthogonal to the authoritarian/libertarian spectrum. Classic liberalism is, I think, more aligned with the right but also profoundly anti-authoritarian. Similarly, the left has a proud tradition of supporting individual liberty but also a strong tradition of suppressing it in favour of collective power.

Corporations of all stripes tend towards authoritarianism though, in my view. It is a natural structure when you have agents using someone else's capital.