The axioms can contradict a particular view of reality. The "scientific" axioms assume that objective reality can be observed (they reject solipsism). Solipsist

The axioms can contradict a particular view of reality. The "scientific" axioms assume that objective reality can be observed (they reject solipsism). Solipsistic axioms don't accept this, only the state of one's own mind can be directly observed so it's the only objective reality under these axioms. Religions accept the existence of one or more gods as axioms, usually with some extra axioms declaring the properties of such god(s).