Hiya.
I was reading over the rules and spirit binding made me think of a “nature-based” religion… Would it be appropriate for a character to use spirit binding while having the faithful trait?
I was imagining a religion based around nature or avatars of nature…
In a setting I ran, we allowed Faithful PCs to summon spirits using Minor Miracle. But it seemed to really be pushing the system into unbalanced mode.
But why mix the two? Just make the religion of your setting be led by Spirit Summoners and forego any Faith at all.
That’d probably work very well 
If you did, just be aware that the Religious LPs in the book may not match your setting exactly. But a dead-simple solution would be to replace the Faithful Trait with Gifted and add in Circination to the Acolyte and Summoning to the Priest LPs.
Kublai has got the general idea down, although those specific suggestions make summoning priests, not spirit-binders (which honestly is still pretty rad).
Acolytes should still get the circulation skill IMO, no matter if you have spirit binder priests or summoning priests circulation is the skill that
A) you would logically teach first since you don’t want some hot-shot summoning/binding something if they can’t make a prison circle for it, and
B) is a task that the preachers would totally delegate, as it seems like a lot of pretty tedious detail work that the higher ups would not want to be bothered with (but would be very quick to point out a mistake in their underlings work)
And then you give the priest LPs Spirit Binding
Replacing faithful is a little trickier with spirit binding as gifted actually doesn’t help them at all (you can technically summon without being gifted as well, but it just requires and extra circulation test every time so I would still keep it in for summoners). You’ll want something that makes the character Immanet/Pre-Immanent, if part of the flavor of your setting involves your priest-caste (or at least the binders) being descended from elves or spirits or something then Fey Blood might be a good replacement off the list. Haunted might be another good one to give em, but personally I’d brew my own. Of the top of my head something like
Spirit Tattoo:
This character bears an ornate tattoo somewhere on their body signifying they are a member of the priesthood that has completed a trial of the spirits. This character counts as Pre-Immanent for the purposes of the spirit binding rules. In addition, they may upgrade one of their free bound domains to a sworn domain at no cost.
Edit to taste.
Conceptually, they’re sort of at odds. Faithful is all about calling upon divine power from outside the world. Spirit Binding is inspired by various forms of animism, which has the divine in everything around you.
I was imagining a religion based around nature or avatars of nature…
So yes, I was trying to work out how to do, essentially, an “animist” religion where the objects of worship are the spirits of the environment rather than a singular distant power…
I once toyed with an idea like that and the way I was going to go was to use the Summoning rules but reskin the categories of beings you could summon to be various nature spirits. So the spirits don’t answer your prayers but you can bargain with them for power.