Perhaps troops led by nobles of the same religion as the priest might not interfere?
Maybe, maybe not. Just because they are the same faith doesn't mean you want to help them, or agree with the actions. It could, after all, be a rogue priest.
If you want to stress that this is not a takeover method for a realm, but for a religion, you could even have troops from the realm the region currently belongs to not interfere if they are led by a noble of the priest's religion. . . .
Wouldn't work in the case of multi-realm religions, where the same religion has members on both sides of the war.