The big difference is that many religious beliefs can’t be tested. They are just believed in faith. In science, nothing is believed. It’s all evidence based and tested. A scientist doesn’t have to reconcile their religious beliefs with their scientific ways because their beliefs are outside the realm of the scientific method. They accept that they don’t have a way to measure or test those things.
There are things in those books that are demonstrably true, but that doesn’t necessarily prove everything in them just as those things that are demonstrably false don’t necessarily disprove everything in them.
It’s just a matter of not being able to observe, measure, or physically test a god’s existence. From an objective standpoint, believing whether a god exists or not is still just a belief.
I’m only trying to show how a scientific person could compartmentalize their beliefs from their studies and to that end, I think we agree that they aren’t incompatible. What someone chooses to believe after that is up to them, because as you point out, there’s no peer reviewed published evidence one way or another.