I've already done a few doggerel entries on this sort of thing, and should do a better job of directing woos there. But I'm going to consolidate a theme that just get so irritating to hear.
Methodological materialism, practiced by science, is an inherently INCLUSIVE philosophy. I don't know where "natural" and "supernatural" started in definitions, but science covers a definition of natural/material/physical that grows whenever we find something new. It wouldn't work otherwise. We look at anything that has effects on the universe. We look at anything that does stuff. That's why we don't bother with invisible, intangible dragons that breathe heatless fire. If something doesn't leave any evidence, why would you believe in it at all?
Take a look at the history of science and its advancement: Then-exotic forms of radiation, bizarre particles, invisible dark matter that can only be "seen" by its gravity, models of space and time that curve or change relative to the observer, etcetera, etcetera, etcetera. There were all radical ideas that are taken for granted today. They were things that would have predictable effects, and when those predictions came true, they were accepted into the mainstream.
The reason we don't accept psychic powers, astrology, universe-designing gnomes, or evil alien overlords isn't just because they're weird. Weirdness doesn't put them in some other realm where Mr. Spock's tricorder can't pick them up. What gets us is that they don't have any supporting evidence. Alleged psychics fail to bend spoons with their minds when watched closely. Astrological predictions don't come true, or are too vague to be worth heeding. Hypotheses about universe designers don't explain anything or make predictions. Evil alien overlords never left behind any bits of metal with abnormal isotopic concentrations or whatever.
"Supernatural" claims that are supposed to actually mean something aren't beyond science, and you can't get us to pidgeonhole something as expansive as science into whatever artificial constrants you like to add to the definition.