When you remove all non-reality based -- mystical elements-- from a religion, what would remain in that religion's philosohy?
It would be a swiss cheese philosophy full of holes.
You're still confusing the implicit causality with the explicit social codes. So here's a concrete example: Kosher rules exclude eating pig meat. We all know why now - Trichinosis. But it probably took the Israelite tribes 500 years of observation to come up with the axiom: don't eat pig meat, because you might end up dead. And so the leaders of the tribes - the Priests - made a rule, that they buttressed by saying "this is rule of God". Lacking a physical explanation, that was the best they could do.
But again, in what way is this "mysticism" as opposed to objective empiricism? You could just as reasonably say that indeed, God doesn't want you to eat uncooked piggies. The fact that the world actually is so constructed is easily ascribed to a deity - and science cannot and would not oppose that, because ultimate causality is outside of its charter.
There are legitimate contradictions between science and religion - the age of the earth, evolution, blah blah. But in many cases, those are controversies within the "faiths" themselves. In the end, anyone can see that much of religion is empirical itself, and that its conclusions regarding social behavior are based on experience and history, and not merely the ad hoc assertions of the local soothsayer - your "mystical" component.
Where the two approaches diverge is this: science has no opinion on ultimate causality, and would not posit one, absent a lack of a method of proof. Religion does, and posits a "faith" that such causality has been revealed through persons and history. It's as good an explanation as any. But the social systems so buttressed have, in the Judaeo-Christian case, borne out as successful. Might be a good "proof" that they really were the "laws of nature's god".
Neither you, nor I, or all the scientists and engineers I have known and worked with could say one way or the other.