Even physics has its faith based science
Science is defined not by where the ideas come from but by the fact that the ideas are testable. In this day in age, where we don't like failing any students, we seem to have encourage tests that everyone can pass. If this attitude gets extended to science it will kill it. What makes science special, is that it is defined by tests that can be flunked. In a word, falsifiable.
So the problem with religion based science is not the fact that religion might be used as a source of ideas, but instead that falsifiablity might be dropped. The primary battle that gets time on the news is intelligent Design. But in physics, there is another theory that equally qualifies: string theory.
An article in slate convincingly makes the argument that string theory is no better than ID. OK, so if we did build a particle colider the size of the milkyway, it could be falsified. But somehow that is a distinction without a difference.