Roman Catholic Church
The Roman Catholic Church survives in the Fifth World, though, like Christianity as a whole, their ancient predecessors might not recognize it as such.
Living amidst the ruins of the Vatican you will find a family that calls itself the Curia. Among them you will find the pope, who can recite the line of his predecessors back to Saint Peter himself. Across the world, you fill find families that still consider themselves Catholics. Many of them tell stories of when the cardinals grew wings and flew away as the birds that bear the same name, with varying degrees of sincerity.
The Catholic Church in the Fifth World does not have nearly the cohesion it did in centuries past. It takes too much effort to travel, and no one has the power to force an “errant” parish to do things differently if they don’t want to. The old hierarchies have, of necessity, given way to a voluntary association of families across the world.
The Jesuits have survived, as well. In the Fifth World they function as couriers and messengers who allow the far-flung Church to retain any sort of communication at all. They bring messages between Catholic families, and from them to the pope, as well as messages from the pope to the faithful. They call themselves “missionaries,” focusing on their mission of keeping the Body of Christ connected, largely failing to even recognize that the word used to mean converting people, much less actually doing so.