Is the fundamental difference between conservatives and liberals related to the perception of hierarchies?

That is the view given in a short article in the latest issue of Scientific American. You can get a summary here

The idea is that conservatives tend to see clear dividing lines while liberals see much more mixing and matching. For example, a conservative may say that someone is either male or female, while a liberal would allow for transgender. A conservative might say that human life begins at conception while a liberal might argue that there is a process by which a fetus becomes fully human. Conservatives might be more prone to believing in racial stereotypes while liberals see more behavioral diversity for a given race.

I will have to give this more thought to see how valid the distinction is.