<pseudo-math> You could define equivalence relations on the set of religious people (RP) and the set of atheistic humanists (AH). In most cases, the people in the sets only interact with (or at least influenced by) other members of the same or similar sets. Turn these interactions into operations on members of the set (a,b in RP, a*b = "a makes b feel awkward/scared/unhappy around a" or maybe something based on social relationships between members). These operations would create new "people" whose characteristics are similar to that of the person who has been molded by the defined social interaction(s).

Starting from a certain subset of RP, these operations could possibly generate the entire set of members (i.e a*b = c in RP, where c has the equivalent disposition as someone who has interacted with b under some applicable equivalence relation). Do the same for AH (using the same equivalence relation), and compare the structures. Under different types of interactions between members, this could reveal some interesting group-theoretical properties. Maybe there is a generating set for RP and not for AH if we keep the equivalence relations from getting too specific. </pseudo-math>

I guess what I'm getting at is that the structural elements of a certain set of people could tell us something about the distribution that the set was pulled from, or even invalidate the need to look at the distribution at all. Maybe the structure is even more important; these sets could pull from the same distribution, but the ideologies that formed these sets could result in drastically different results from operations (social interactions or relationships) between members of the set. Or we could see if only the generating members of the set were pulled from the same distribution, but the social interactions between them created a set member not from the original distribution, resulting in the set having to pull from that distribution also.

Anyway, this is probably not coherent or useful at all, but if nothing else it did lead me to the work of Harrison White on mathematical sociology:

A good summary of White's sociological contributions is provided by his former student and collaborator, Ronald Breiger:

... ... (2) models based on equivalences of actors across networks of multiple types of social relation; (3) theorization of social mobility in systems of organizations; (4) a structural theory of social action that emphasizes control, agency, narrative, and identity ...

This was particularly interesting:

For instance, we are told almost daily how the average European or American feels about a topic. It allows social scientists and pundits to make inferences about cause and say “people are angry at the current administration because the economy is doing poorly.” This kind of generalization certainly makes sense, but it does not tell us anything about an individual. This leads to the idea of an idealized individual, something that is the bedrock of modern economics.[6] Most modern economic theories look at social formations, like organizations, as products of individuals all acting in their own best interest.[7]