The difference is that science doesn't tell you to dogmatically follow axioms per se. For example, the constancy of the speed of light is an axiom of Einstein's theory of relativity. Evidence that disproves said constancy would eventually lead to revising the theory, just as Newton's axioms were eventually replaced by Einstein's relativity. That's not dogmatic following.

On the other hand, the virgin birth of Jesus (for example) is a dogma of Christianity. From what we know about our world, a virgin birth is not possible, not with the technology that was available at the time the Bible was written. Christians still accept this tenet of Christianity at face value, despite the ample evidence against it (evidence they would never ignore in other aspects of their lives). That's dogmatic following.