Blogger N.S.Gill is apparently asked some version of this interesting question often enough that she has compiled an FAQ on it. She writes:
Almost every week I simplify a welter of contradictory stories for the Myth Monday. … Some readers ask how the ancients reconciled seemingly unrelated versions of the same event.
Historian Charles King (The Organization of Roman Religious Beliefs, by Charles King; Classical Antiquity, (Oct. 2003), pp. 275-312.) provides insights into how the ancient Roman polytheistic, pagan religion worked that make sense to me, so I’ve extracted ideas from his 39-page article into an FAQ – Did the Romans Believe Their Myths?
I imagine the question arises from people used to the Christian approach to life, where beliefs determine behaviour and worship.
But I have read that the reverse was the case in paganism. It didn’t matter what you thought personally — who cared? So long as the right rituals were carried out, the sun would come up in the morning. Temples didn’t gather congregations; they were more about doing things like sacrifices.
In a sense an ancient temple was more like a nuclear power plant than a church. It doesn’t matter whether you believe in physics in the former; only what you do.
I wonder if any ancient source actually says this?