They are independent of each other, Science is based on facts and religion is based on nothing but belief. How can science ever limit itself to a 6,000 year old earth, intelligent design and a bible of rules.
Science is completely on their own here. If it is not science then it cannot be compared on the same issues as the other. One is real and the other is shit

According to the von Neumann–Wigner interpretation of quantum mechanics consciousness is an essential component of reality. This does not prove any religious belief correct, but certainly leaves a lot of scientific room for religious beliefs.

Not really, because religion is the end of inquiry. As as soon as you assign a divine intent, you stop searching for rational answers. Religion tells you how it is, science is a means of determining how it actually is. That doesn’t seem particulaly compatible.

Religion doesn’t have a particularly good track record arguing with science.