There is stuff out there that is not computable (in the technical sense), there is stuff out there that is not provable (in the technical sense) and there is stuff there that is uncertain and non deterministic and non local (in the technical sense). These are mathematical facts and accepted physical theories.We gained these insights through a rational process.
Perhaps there is a vagueness about what rational means, here is an example of how I think about this: Godel demonstrated a mathematical fact that is true and not provable in mathematics (skipping "some"
details here). The fact that it is true can be "rationally" explained to and comprehended by, a bright ten year old.
If you want to call those aspects of reality that can not be proved, determined, computed etc... supernature, that's Ok. Somewhat overloaded with meaning but Ok. I do not think however, that this supernature has enough "volume" to contain a religion in it.