Actually, the characteristic of science is that it deals with testable and retestable knowledge, not its naturalism.
I have already pointed to the naturalistic, but patently non-scientific cosmology of Lee Smolin, which shows the non-congruence between science and naturalism in one way.
One can see it in another way also: many early scientists did experiments in what is today called 'the occult'. They gave no reproducible results--or rather gave the oft reproduced result that the ceremonial manipulations did nothing--but the attempt shows that the supernatural is not outside the domain of scientific investigation.
Or they showed was that spirits were not natural phenomena.
I didn't say science talked about "naturalism". I said science deals with the natural world, meaning the study of things that actually exist/existed/might exist. Religion on the other hand is the study of the supernatural/paranormal/beliefs something that can't be manifested or proven either way.
Science is physical things, while religion is all mental.