i disagree. i’d posit that science finds the truth about the cosmos. religion offers a lens through which you can interpret and apply the truths that science has discovered.
i think what you’re describing is how various practitioners of each have traditionally presented the tools of science and religion.
I think science and religion are even less coupled than that. The newest gravimesobaryon discovered through the LHC probably doesn't have any bearings on religion, and rituals such as Ramadan aren't performed for a benefit based in science. One's moral values/axioms and one's factual understanding of the universe can largely be separated, but a lot of people nowadays seem to heavily conflate them.
I think it’s because some people wants to impose their values on others, especially if it gives them an advantage in society. Moral values are fluid and can be manipulated, facts are not. Religion used to shroud values into fictions and present them as the truth. But, because science are demystifying most of them, leaving only the moral parts, people are starting to see that moral values are relatives, not absolutes, and it involves only oneself. So now, they want to dress science as one of the other religions, something that is wrong.
Religion says it's the truth, and wants you to follow it.
It's the same thing as giving a fish or teaching how to fish. Receiving a fish is convenient, but I'd rather not depend on someone for food.