Science isn't naturalistic by its nature. To the contrary, if for some reason everybody born on a certain day were very similar in very definite ways, science would figure this out. If you could with a few words whether a spell, prayer, or incantation cause a very real consistent and repeatable effect on the natural world, even if these effects were, as far as we could tell causeless, we would still measure and study it. We could quite literally get prayers down to a science.
For example, quantum phenomenon are often uncaused. In reality there is no reason it should do what it does, but we can measure them very exactly. If supernatural things had such an effect on the real world, they would look identical to quantum effects.
Now, why then do we never find such supernatural causes for things? Why don't we prove astrology, religion, prayer, magic?
In science, we test our ideas about reality against the natural world and figure out what sticks. It isn't science that has a vendetta against your favorite pet fantasies, reality doesn't back them up because they are false. Sorry, but science just seems naturalistic because only naturalistic explanations exist as a part of reality.