"shouldn't that work equally on both liberals and conservatives? "

Not necessarily,,, because humans have the 'gift' of being able to look a 'sound' argument right in the eye and refuse to accept it. Rationality is often used in the sense of 'rationalizing'.... turning a series of points in ways to suit pre-digested conclusions.

Now, *IF* one has a position based on false premises, then it is easy to arrive at a conclusion that follows 'logically' from them. (A basic idea of philosophic logic... "From false premises, anything follows")

One of the things about many conservative principles is that they have the answers they want, and just need the proper questions...and rhetorical devices.

Liberals are not totally immune to this malady, but they 'tend' to be more willing to seek 'truth', no matter where it leads.

If I had 2 hours and were not leaving town in the morning, I'd go on at interminable length about how the two thought processes have some very different components. (hint- much religious thought MUST not stray TOO far from various positions-- think Galileo)