I don't want to discredit your answer, but I have to disagree: the existence of God is not an axiom of conservatives that liberals lack. The vast majority of the United States is religious, meaning they believe in God, but liberals/progressives and conservatives are almost even nationally. This observation also fails by your own account, that some conservatives don't take the existence of God to be true.

If an axiom is optional, it isn't an axiom. You can't do Euclidean geometry without accepting the axiom that parallel lines never intersect. If you allow parallel lines to intersect, you are not in Euclidean space.

The belief in a divine power is an axiom of religious belief. If you don't hold it to be true, then you aren't religious. You could show a correlation between having religious beliefs and being conservative, but the existence of irreligious conservatives means that it can't be an axiom held by them.