The very notion of science itself is incompatible with religion.

No it isn't. Science itself is a kind of religion, with beliefs and practices adopted on faith.

Science takes as its central premise that nothing should escape testing or questioning.

That sounds like a recipe for The Inquisition.

But the real central premise of science is that observable phenomena can be understood, explained, and even predicted in terms of testable theories and models. The notion that the world can be understood in theoretical terms is an unprovable belief. It's a successful belief, but it can't be proven.

Moreover, the method for constructing scientific theories -- the Scientific Method -- is also adopted on faith. There is no guarantee that it will work in every case.

Part of the problem that we face in science is that the theories we are obliged to construct are often mathematically subtle and abstruse. Most lay people don't have the math to understand the mathematical models which comprise many of our best theories.

One of the reasons people like to debate Darwinism is because there isn't very much math in it, and so the lay public can readily understand what it's saying. Lay people don't take issue with Newtonian Gravitational Mechanics or Einstein's models because they are written in pure math -- a language most lay people don't understand. More to the point, they don't even take issue with population genetics, since that's mostly about calculating probabilities associated with breeding. And that was a subject founded by a religious cleric who bred peas.