In interested in if there was ever conflict, both between individuals of the same city/cult center and the centers themselves with other towns.
From previous answers, it seems highly unlikely that cult centres within the same pantheon would fight wars, considering even worshipping gods from different pantheons was usually accepted. This is discussed by u/Trevor_Culley and others here, and in this thread our u/cleopatra_philopater writes about it with a focus on Greek religion. You might also be interested in this answer by u/alricofgar on whether there were religious wars in Antiquity