It's impossible to model the complexities of the human condiition fully. However, as the atheism debate points out, the system should be able to model the fact that both religious ideas and cultural affinity effect a person's core identity.
As has been said, you have Jewish Atheist and Jewish believers, who are more or less not at each other's throats. However, unlike some, I don't think that's a particuarly unique situation.
I think pretty much every culture has it.
What could and should be done is to assign each pop a primary identification. More 'philosophical' pops (and probably fewer at this time) might have their religious beliefs, which included Atheism, be ranked as their #1 concern. The majority of pops will probably have their ethno-cultural identity ranked as their #1 concern.
So, whereas a Jew in Europe, or a African slave in America might both be an Atheist. You don't have the odd situation of either being more concerned with the religious debates and writing each other letters and bringing down the Pope than the fact that say Progrom is comming for one, and slave catchers are comming for the other. (If they are more conserned with their cultural identity than their religious.) Even if all things being equal, they are both Atheist.