While non-religious and religious are reasonably disjointed sets, atheism is not disjoint with religious. That is the set containing the union of atheist with religious is not the null set.
I remember a joke in the book where two rabbis are discussing the issue of god's existence during the supper, at the end, they both agree that god must not exist and then go to sleep. At the next day one rabbi finds the other doing his early prayers and confounded asks him why he is praying if there is no god, to which the other one answers "what does praying has to do with god?".