You are making it much more complicated it is. All prayers, regardless of which religion they originate from, reach the same almighty in heaven. Never refuse any prayers. It only shows narrow mindedness and ignorance of history. If I was struck by a Mack truck and in critical condition in a hospital, I would welcome prayers from anyone and everyone belonging to any religion.
God isn’t stupid, nor is He confusion. He might CHOOSE to play along in the case of someone being guided into an accurate faith. But some kind of kumbaya universalism is simply wrong, and the devil likes it.