Religion would definitely play a rule, do it’s hard to say to what degree. There may have even been multiple coexisting religions, perhaps fully polytheistic situations. Catalhoyuk is a fine example with worship surrounding a bull, as well as a female deity. You typically see both male and female aspects represented in the Neolithic sites.
I believe that ritual would be a major component of a Neolithic Society, based upon grave goods and what’s been found at sitea. I do agree that the detail of each religion may not need to be addressed in so much detail, though personally I would love absolute configurability LOL
to balance the importance a religion with ease of gameplay, using a simplified set of religious variables might be useful:
Focus*: Sky, Moon, Sun, fertility, death, hunting,etc
Religiosity: casual, moderate, devout, fanatical
Priesthood: male, female,all
Sacrifices*: none, objects, animals, people
Ritual frequency*: as needed, daily, monthly, seasonally, yearly
*= check box for multiple options.
A simple tab with something like this would allow both easily programmability and the ability of the doves to Simply add some changes to the behavior as a result of these simple variables. For each Focus, you might also have a option of god, goddess, neutral gender God, or just spirit.