Make the worship-barrier non-uniform across the world. In places where worship is weak and/or improper, the barrier weakens, letting demonic entities slip into the world. This creates a highly obvious way for local priests and worshipers to get negative feedback when they do it wrong, and for the centralized authority of the church to figure out where to send inquisitors.

I would think that such inquisitions would be less violent than real-world ones. After all, most heretics would probably willingly repent their heresies when they see that demons are getting loose in the countryside. I'd imagine it would be more like a remedial religious training program to get everyone back on the right path. The tangible threat of demons is the stick, the church only needs to offer a carrot.

This would also help explain why there are few overland trade routes that circumvent the Realm Gate network. Who knows what horrors roam the godless wastes?