The sentence "Frodo carried the One Ring to Mount Doom" is not literally true, but it is true within the fictional narrative of the Lord of the Rings. You can simultaneously believe it and not believe it, in a certain sense, by applying the so called "suspension of disbelief", a mental mechanism which probably evolved to allow us to consider hypothetical conterfactual beliefs for decision making and which we then started using to make fiction.
I think that theists like Robert Aumann who support the non-overlapping magisteria position are doing something similar: they accept "the world is 15 billion years old" as an epistemic "Bayesian" belief which they use when considering expectations over observations, and they apply suspension of disbelief in order to believe "the world was created by God in six days" in the counterfactual context of religion.
Just came across this interview with Robert Aumann. On pgs. 20-27 he describes why and how he believes in Orthodox Judaism. I don't really understand what he's saying. Key quote (I think):
Anybody have a clue what he means by all this? Do you think this is a valid way of looking at the world and/or religion? If not, how confident are you in your assertion? If you are very confident, on what basis do you think you have greatly out-thought Robert Aumann?
Please read the source (all 7 pages I referenced, rather than just the above quote), and think about it carefully before you answer. Robert Aumann is an absolutely brilliant man, a confirmed Bayesian, author of Aumann's Agreement Theorem, Nobel Prize winner, and founder / head of Hebrew University's Center for the Study of Rationality. Please don't strawman his arguments or simply dismiss them!