The Apostles of Eternal Light believe that ghouls are the next stage in human evolution and that we "should not resist the idea." They use radiation traps to turn themselves into ghouls. Unlike the church in Megaton, this church is against the great division and thus are opposed to blowing up the Megaton bomb.
The Lone Wanderer will learn of the cult after seeing a holy water pamphlet on the door of their house in Megaton, by asking a few of Megaton's inhabitants, or by talking to Brother Gerard. After a deal is made with them or they are killed, the pamphlet will still appear on the house door.