Actually that part felt reasonably well thought-out from a world-building perspective to me. If one was to lay odds on which of humanity’s institutions are likely to be around for centuries to come then it would make sense to put one’s money on the ones that have already endured for thousands of years.
You don’t have to like the Catholic Church to acknowledge that it definitely has some staying power. Even Herbert’s Dune series hints at it (i.e. references to “The Orange Catholic Bible”).
