"Science itself is irrational or mystical. It's just another faith or belief system or myth, with no more justification than any other."

I think I would ask the speaker whether he'd rather take off in an airplane that was designed using the laws of physics or whether he'd be just as happy with an airplane designed using "spiritual, mystical, or inner ways of knowing" that "feel right." :-)

Although I agree that many truths and experiences seem subjective in nature, we all live as if there is an objective reality.
Amanda