> In one domain, they are skeptical and thorough, but in the other they’ll just take anything at face value without questioning it.
Belief in a God doesn't require that the believer never questions their own faith. It is possible for them to question it, do their own experiment, and determine that there is a God. They could even start as an atheist scientist.
> How do they even know which god was responsible?
Lots of religions have an answer for this. Probably all of them, but I am only familiar with so many. Sounds like you have taken religion "at face value" and could be more "skeptical and thorough" in your research/understanding of them, to quote yourself.