Respect for reasoned enquiry (including science) is not based simply on belief.I don't know why you mention science and religion as if the debate between atheists and theists is a debate between science and religion. If the atheist in the debate is a believer in scientism or an empiricist it may end up as a religion vs science debate but scientism is a belief that is not atheism.
It's based on the observation that it works better than any presently known alternatives to explore, describe and seek to explain the world external to the self aka objective reality.
I suggest that the reason it doesn't work for supernatural beliefs is that the supernatural isn't found in objective reality ─ if it was, it would be natural, not supernatural ─ and the only manner in which the supernatural is known to exist is as a set of notions in individual brains.