My players treat Cult as a bad word, which was interesting to me. My take was much more positive; a cult was a small group of worshippers whose practices weren’t cultural, and whose beliefs were secret. Theirs were more negative; a cult was a group of worshippers of unclean habits, whose deeds were dark. That led to a few miscommunications; the somewhat morally-grey Cult of Luth, the keeper of secrets, venemous insects, and scholarship is an enemy religion to them. But really, I intended them to be pretty adventurer-friendly! Alas, alas. But to me, this makes the most sense.
D&D is cultic, but for some reason the published content doesn’t recognize this.
Think about it: clerics have private access to spells, granted as they delve into the underworld and gain wealth and knowledge. That doesn’t sound to me like a parish parson or a church-sponsored exorcist: it sounds to me like a devotee of Bacchus or the Chosen of Anubis. The usual D&D milieu puts faith off to the side, because let’s be honest here, we’re just in it to game. Of the characters which are godbotherers (like clerics and paladins), their advancement isn’t related to their deity in any way save the nature of their powers.
Under this rubric, warlocks are not just taught or sponsored by their patrons, they are marked. Their powers refresh much more rapidly than those of other casters (save monks and certain high level characters of other classes). This matches the at-will and random refresh powers of other monsters. Clerics have something similar in their channel divinity, and lo and behold, it does a good job of making them less like other casters, less like other characters.
Reindeer Games
So, okay. D&Deities sponsor cults. What does that mean for us? For one thing, the nature of being a “divinity” isn’t a discontinuity in our NPCs. It’s perfectly okay to introduce “deities” as creatures beyond normal monster power levels, but being a deity and being worshipped have little to do with one another, and we can choose to do these things separately. This is great, because it frees us up to have philosophies alongside individually worshipped beings alongside pantheons for our set dressing without needing to worry about clerics.
Your fighter and your cleric both have the same interest in finding temples. Regardless of what the overall religions (, politics, trade guilds, …) in your campaign, a cult of Aphrodite and a temple to the gods are very different things! You should feel free to introduce continent-spanning power groups, but the existence of a character with spells doesn’t require that you replicate them in each town.
The central mystery of most cults should allow a character to befcome first level clerics (or warlocks, or maybe other classes like paladins or druids). That is, if your character drinks the Blood of the First from an invested priest of same, then they can become a first level cleric by sacrificing their latest level of fighter. Because they spread in this hands-on way from cultist to cultist (and not all cultists, by the way: think “followers”, name level at a minimum), they have geographic locality and specific NPC relationships.
And by the way, participating in this mystery doesn’t work for everyone. Some people just aren’t cut out to be the faithful.
Why Temples?
So let’s say we go with this. Deities have whatever powers we give them; clerics have whatever powers they discover on their own, and the relationship between the two is one of initial sponsorship and mentorship, but not an ongoing source of power except in rare cases (avatars, chosen, prophets: in-game statuses all). Temples which don’t actually empower their priests (“All of the olympians” instead of “The cult of Zeus”) exist for the same reason universities do. They function as a sort of trade guild and, like a trade guild, have a lot of officiants in positions of power who are not actually any good at the underlying guild’s business. Priests, in other words. They’re a sort of theoretical scientist in a world where you could be an engineer: cultic participants might be seen as dangerous zealots, short-sighted or mad, while priests are merely devout and wise.
This means that when you go into town and get spells cast at the temple, you’re likely interacting with a mercenary, not a townsfolk. This might be a town where a Hearth-tender of Hestia is doing her thing and keeping the temple, but it could also be a town with a well meaning parish priest — but also a priest of Hermes passing through on a frequent basis!
Similarly, a temple might be built in a holy place or a historic place. That holy feature might be more important than the shrine atop it, to adventuring characters. The townsfolk might go to temple services for community and to learn the theology and cosmology in which they’re set. But the heroes know to stop in the sepulcher and pay their respects to the bones of Saint Erasmus if they have a curse they need removed, or to travel two towns over to remove diseases at the Waters of Genesea.
Mono-, poly- and heno-theism
This agnostic stance on the relationship between religion and the Cleric class pays off in spades. Regardless of the theology of your campaign, all you need to do is introduce a division in the faithful which associates power with danger and self-determination (you know, PCs?) and let the rest unfurl. Maybe your church structure only elects Clerics to positions of power, that’s a fine choice. But maybe Clerics hide their powers (but not their faith!) because the Church is a loose association, and suppressing that factionality lets things work better.