The parish provides a sufficient population that enables social proof to convince people automatically of the correctness of believing and belonging. It's not that the priesthood makes people believe things - it's the people, and the social proof and the social pressure that does this. The priesthood gains political power (which all men yearn, consciously or not), and when co-operate with the state provide a channel of mass control and communication. Thus the people perpetuate the belief, and the state has no incentive to intercede.