Jesus was complex. Some might argue the most complex person in all of human history. As such He is difficult to categorize.
There is for every instance of something Jesus said, (not exactly but frequently) another instance of Him saying something quite the opposite or at least somewhat contradictory.
This is a characteristic of his teaching style, his own beliefs/philosophy and His existential reality--(i.e. all humans are by nature inconsistent. Jesus was a human and therefore Jesus was inconsistent.) Now being inconsistent is not a bad thing. It merely tallies with the fact that Reality is complex and being a human living in the fishbowl of such a Reality, you will be, at times, inconsistent.
So what does it mean to say Jesus was liberal or conservative? I would argue that these terms both apply to Him. There are instances of both throughout the N.T. and that is a solid fact.
I argue in one of my Hubs: https://hubpages.com/religion-philosophy/Jesus-Was... that He was politically incorrect. But in what way? Tory or Democrat? This adds to His complexity.
Surely there are wonderful scholars who have clarified these paradoxes and contradictions of the person Jesus and if we turn to some of them we will get a much better answer than one I might give.