>>11324052
First thought is just the standard trope inversion of "church secretly evil", so evil church secretly good. Something like they only support demonic invasion through tending to the wounded or displaced, and it all stems from their belief that corruption is the convergence of humanity and demons, any forced sex slavery arrangement is temporary, and a fully corrupted humanity will live as equals in demonic paradise. Exact theology is probably not that important to the player and protagonist compared to what NPCs they're interacting with. Maybe have the ringleader or a cute nun succubus or incubus (dealer's choice) immediately suss out the PC and instead of raising the alarm offer the macguffin in exchange for taking temporary vows or otherwise providing community service.
From there, the world's your oyster. Sermons that devolve into praise kink/body worship with the protagonist trying to figure out how much is just honeyed words and how much is a cloistered virgin seeing an unclaimed human up close for the first time. Regular soup kitchen work to cast doubt on PC's worldview. Sex soup kitchen work about having to chug demon cum left in the used bowl as a thank you. Vignettes about having to handwash weird demon underwear or outerwear. Nonsexually massaging sore sex demons who've been fucking all day. Sucking a demon dong because that's demon charity idk.