Well, they do compartmentalize. They're also fairly unhappy, but not to a level where they're going to disrupt their entire social sphere and be ostracized (at best) from polite society for speaking up.
(Knowledge level: have talked to an n > 7 number of Arabs from the Arab world, usually Jordanians, Palestinians and Egyptians.)
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!