So, my interest in the bronze age middle east is pretty narrow and outside of the timeline of the base game. However, I would like to discuss rival religions. For example, there were two early bronze age cities: Umma and Lagash. The patron god of Umma, Shara, was a minor war god; and the patron god of Lagash, Ningirsu, was a god of law, scribes, farming, and hunting. These two cities were so often at war that their two respective gods were considered to have hated each other and were held responsible for their city’s victories and defeats. Hence, they formed a mythological rivalry. Although these gods were much older than the early bronze age, it is only in the EBA that they came into major conflict; so, I don’t know if the same could have happened in neolithic times or not. However, it would seem to me that going to war with another tribe with a different religion to your own would make your citizens more intolerant of that religion by proxy.
Think of Civ VI. If you try to proselytize in another city with your missionaries and apostles and the ruler of that city tells you to stop, but you continue, then you receive a diplomatic penalty with that character. This system seems to work on the large scale, but on a city-building level, I think the mechanic would be too personal and not representative of a communal response to proselytizing. So, I think that hatred of rival cults would be an alternative, much like how the early followers of Seth in Prehistoric Egypt (game) hate Horus and result in inevitable conflict with that cult.