"Non-overlapping magisteria" is absolutely the right phrase to use when describing Aumann's defense of his religious beliefs. Further, I'd point out that it seems like Aumann really wants Judaism to be true, in that he enjoys being Jewish, and feels that he'd lose tangible benefits (such as being able to enjoy the sabbath) by becoming a secular person. I think it's somewhat common for religious people to feel threatened by the thought of losing something in the process of becoming atheists, and that this fear can push them into adopting positions (such as the non-overlapping magisteria position) they wouldn't have otherwise adopted. I'm not sure that most religious folks adopting such positions for such reasons are aware that these reasons are their true rejections of atheism, though. Sometimes, making people feel comfortable (with, for example, the idea that they can have supportive social networks without being religious) is half of the battle.
On a personal note, I was raised in a religious family, and I always enjoyed the peace and warmth that came along with the Christmas season. Since becoming an atheist, I've found that I can get the same warm feelings by being nice to others, and by drinking spiced black teas. Similarly, I still like gregorian chants just as much as I did years ago. Very little is lost upon becoming a secular person.
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!