Clerics want extra benefits for being in the church. If they want it, they should have to pay for it.
I'm not really planning on it, but if I did allow the Church as a "patron," I'd actually use Matt Riggsby's excellent rules in Dungeon Fantasy 17: Guilds.
The Church would fall under the rules for Congregation (p. 10-11), with exceptions.
GURPS DF Felltower doesn't use the Bless spell, so "Blessings" aren't a thing that the Church could provide.
They are a bit more free with spellcasting, though, so those ARs would be at +2.
I might tweak the AR roll so it is below 3 for Rank 0, just to avoid everyone asking to make a roll for many different things each session. Or set a cap on requests.
Otherwise, the Church would likely function indentically to Matt's outline.
Any details I'm missing? I don't think so, based on my (admittedly not recent) reading of DF17.
I reiterate that I'm not planning on switching to the DF17 system, not as yet. Mostly becuase I suspect 3 of my players would read DF17 and spend a lot of time and effort on maximizing their benefits from the organization(s) involved, and the rest of the players would read none of it and use none of it except to be told what to roll. That doesn't sound like a good use of my between-game time (when I'd be reading emails about "Can I ask for [this]?" or "I want to make a roll for [that]") Or my early-session time doing the same.
But this is likely how I'd do it.