I think you'd want a range of faiths, or at least a range of organizations representing various faiths that would allow for latitude in playstyle, goals and whatnot.
This. As a member of a minority religion, I am painfully aware of what happens when one religion declares its members are "the faithful", and declares all others not worth defending. When you say "the church", do you mean that there is only one church?
There are all too many historical examples. In some of those examples, one form of Christianity was on the dominant side, and bad things happened to other kinds of Christians, and also all others, such as Jews. In other examples, Islam was The Faith, Muslims were The Faithful, and bad things tended to happen to all others - perhaps not quite as bad to Christians and Jews, fellow "People of the Book", but worse for others (such as animists). In the USSR, Stalinism held a role equivalent to "the faith", only atheists were promoted to high Party office, and some Christian activists (and many Jews) were sent to the gulags.
Would a defender of the faithful also defend the passengers of the St. Louis on its voyage from Hamburg to Cuba?
In the Forgotten Realms of D&D, I would happily play a cleric of Lathander working hand in hand with a paladin of Bahamut, or vice versa. I would prefer a game in which they sometimes ally with less closely co-aligned cults, such as chaotic good Corellon or Tymora, against shared enemies - they have their differences, but they're allies against Tiamat, when necessary.
As it happens, I recently played a paladin with the Ancients oath (dedicated to life and liveliness), working closely with a warlock of the Raven Queen (all about death), against their mutual enemy: an empire using a particularly nasty form of necromancy. The paladin didn't like the warlock's use of Hunger of Hadar... which brings something fundamentally *wrong* into the Prime Material, something which doesn't belong here... but better to live with it, a minute at a time, than risk the consequences of an Imperial victory.
In Call of Cthulhu, perhaps a rabbi works with a priest of Ganesha; maybe the combination of Vedic scriptures and Kabbalah lore is necessary to defeat the cultists of Nyarlathotep. In "Beyond the Supernatural", I'd play the Nega-psychic, the atheist skeptic whose dis-belief in magic is so fervent, so strong, that it can remove demons and other cross-dimensional incursions. (It doesn't just banish them. It *retroactively* negates their existence. "That never happened.") The rabbi and the priest of Ganesha find my "faith" annoying, but they work with me for the greater good.
In Middle-Earth, the PCs could be a team of Istari, all "faithful" to the Valar. The story would have to fill in some details which Tolkien did not elaborate. In this setting, there really is only one faith, and those who don't follow it, don't follow any other religion either (for example, Frodo had no point of comparison, when Faramir's rangers, before a meal, ritually turned to face West). But even Sam could invoke Elbereth, without much understanding of who she was.
Meanwhile, in Narnia, there is at least one worshipper of Tash, who turns out to serve Aslan. Those who sincerely worship Tash, are still better than the hypocrites who turn to "Tashlan".