It’s a worldview that reproducibility goes out the window once you introduce supernatural forces. If the weather where actually responsive to a god who regularly changed things because they got mad, then it would be inconsistent over short time periods.
It does classify things that are reproducible and testable as part of the natural world even if we don’t understand them such as gravity. Finally things that don’t have a detectable influence don’t exist.
This is subtly different from materialism or physicalism which both define how reality operates.
I cannot observe propositions or truth claims or numbers or...
Besides, what is "natural" and what is "supernatural" according to naturalists? [0]
Of course you can.
> what is "natural" and what is "supernatural" according to naturalists?
It changes over time. At the moment, "natural" is anything that can be accounted for by quantum mechanics and general relativity, and "supernatural" is anything that can't: Ghosts. Demons. Deities. Telekenesis. Stuff like that.
No, that is not what naturalism is. That would be circular. Naturalism is the philosophical stance that things that cannot be observed do not exist.
Alleged supernatural phenomena cannot ever be definitively ruled out (because new observations may confirm their existence) but to date there has never been an alleged supernatural phenomenon that did not have an adequate naturalistic explanation.