Science is based upon certain simple but deep philosophical assumptions: there is a real world outside of us, we can agree about what its phenomena are, and we can explain these phenomena using mathematical theories that are the same in all times and places. These theories are mathematical models of physical cause and effect or, if not, can be transformed into mathematical models of physical cause and effect. “Physical cause and effect” is itself a very deep concept, not in the least related to pre-modern theories of causation, and that only becomes more mysterious the more we learn about it, e.g. in quantum mechanics. But the essential idea that things don’t happen without a physical cause is always present.
Science cannot turn around and justify the assumptions upon which science itself is based. Therefore, it is clear that human thought is not something that can be explained by science. This is a very fundamental point that somehow seems to escape people who would like to believe that science can explain anything, or that Nature is “nothing more” than physical cause and effect.
If science cannot explain thought, then if religion is an inescapable category of thought, science also cannot explain religion. And religion is an inescapable category of thought.
The most that can be argued on the other side is that science doesn’t require justification (this is the essence of Quine’s “naturalism”). But if science doesn’t require justification, then neither does religion. And historically, science did require justification, and did obtain it.