Not believing in climate change is relevant to thinking about whether someone is likely to be a trustworthy source because not believing in c.c. means we should be skeptical of that person's writing and conclusions. It's equivalent to believing the world is 8000 years old, or evolution doesn't exist, or jesus rode on dinosaurs.

It doesn't have anything to do with liberal or conservative. It has to do with being educated and drawing reasonable conclusions about the world.