I'm looking for a phrase which essentially means questioning a belief you share with someone, but that other person has an almost unshakable faith in that belief, so your misgivings fall on deaf ears or they try and convince you otherwise without really taking into consideration your points.
Not necessarily religious, but it could be for instance, questioning the negative impact of legal weapons to a friend in the NRA
Best Answer
You could use the expression it's like talking to a brick wall.
It's an established idiom listed in some dictionaries, and it means that you can't get through to the other person.
Another applicable expression might be teaching a pig to sing, from a quote attributed to Heinlein – especially if you find yourself getting frustrated in your efforts.