More like "circular effects"
Not necessarily. True enough that non-natural causes currently are considered outside the possible limits of scientific examination (and have been since long before Darwin). IOW they violate the "nature of science". However the nature of science is subject to change.
For instance it was once a presumption of science that force could only be transmitted by physical contact between particles of matter. Any force that might have been proposed to act a distance or propagate through space would be considered "occult" and unscientific (or "unphilosophical" as they would have said back then). Indeed when Isaac Newton proposed a force of gravitation with exactly such qualities it was, initially, widely rejected as an "occult" force.
The thing was, though, that Newton's law of gravity actually worked, and was extremely useful in furthering scientific research. The lesson here is that a good (objectively useful) theory or law will never be rejected because it violates the "nature of science." Instead our understanding of the "nature of science" will be modified or expanded to accommodate the successful theory.
Now I can't imagine how a scientific theory incorporating supernatural forces could possibly work, nor have I ever known anyone else to describe how it might. Maybe in can work, somehow, but someone needs to SHOW us how it would work. IOW what is needed is a genuinely useful scientific theory that incorporates non-natural causes. Only with something like that in hand can you enter a successful plea for a fundamental change in the understanding of science.
Or you can simply demand that the entire scientific community radically modify it's understanding of science and it's boundaries without offering any reason they should do so. You can do that till you're blue in the face and fall over.