As far as I can see, there are many possible ways that religion could manifest itself in each created Dwarf Fortress world. Personally, I think that as many as possible should be implemented, and the player given the choice over which aspects of religion go into his world.
There are many different variables that could go into defining a religion in Dwarf Fortress, and I think that if a complete and holistic religious system is to be added to the game, that it would be wise to flesh out as many different possible types of faith that could go into the game. For example: one of the chief defining attributes of any religion is what sort of Deity or deities, if any, its adherents worship. Here there are many possibilities.
For example, do the adherents of a particular faith believe in polytheism, a belief in many gods; henotheism, a belief in many gods who exist under the dominion of one central God; or monotheism, the belief in one, supreme Divinity?
There are, of course, different conceptions of gods or God, even under such divisions. In terms of pagan gods: are the gods immortal, like the Greco-Roman pantheon; or are they mortal, like the gods of Norse Myth? Do they have real physical bodies, or are they shapeless spirits who take whatever form suits them. Are there only a few important gods, like the Olympiad; or are there also numerous minor gods, of lakes, rivers, forests, rocks, trees, households, et cetera? Do a person's dead ancestors become gods? Are certain animals considered to be the sacred avatars of gods? Are the gods generally a force for good, justice and order; or are they, like the Lovecraftian Elder Gods, forces for amorality, insanity and chaos (I'm looking at you, Armok)? or are their both gods of light and gods of death? or perhaps the gods remain morally ambiguous? Do these gods exist of their own power? Or are their abilities reliant on the faith of their followers?
In terms of a monotheistic God: is the Deity a distant, cold, deistic God? or a personal God who takes an active role in the world? Is God loving and life-giving? or a cruel, over-bearing tyrant? or a mad, gibbering, Azathoth-like horror? Is God an actual, individual being? Is God a sort of composite being, of whom we all form a tiny part? Is God the universe? Is God a kind of energy, like "the Force" that permeates the cosmos? Is this God male, or female, or sexless? If sexless, does this God has masculine or feminine tendencies, or is it an amalgamation of both? or is it truly neuter? How is this God usually represented? Are representations of this divinity even allowed?
If there is one God, to whom a religion directs all its worship, are there also patron saints / angels, for whose intercession one can pray? Are there demigod-like creatures, similar to Tolkien's Valar, who rule the world under God's command?
Then there are many other questions to ask about a religion, such as rites of worship, priesthood, ecclesiastical structure (if any), codes of ethics, scriptures, dogmas and canons, different sects and orders, and a whole slew of other possibilities that would need to be defined.
These are all questions that would have to be answered, I think, to have a fully defined religion. Such a complete system, with many different possible kinds of religions, would be, I think, best for Dwarf Fortress.
I also happen to think that players should have the ability to set whether or not certain religions are right/wrong: perhaps all the myriad members of the polytheistic pantheon are the true divinities, regardless of what the foolish monotheists say? or perhaps it is the monotheistic God (or one of them at any rate) which is the one true deity, all others being false? or perhaps the world is ultimately nihilistic, there are no gods or God, or any transcendent truth? or perhaps the truth of the matter is never ultimately defined, and is left ambiguous, so that the player could play many different characters of many different faiths without knowing which one (if any) was correct?
It would also be interesting to being able to set agitative preferences, i.e. do we want this to be a world where all the different religions get along, sitting around the camp fire roasting marshmallows and singing "Kumbaya"; or do we want it to be a world where religious tensions exist, but rarely come to bloodshed unless some political entanglements are involved; or do we want it to be a world where all the different religions hate each other, and resolve all their theological differences on the battlefield (God exists by two take downs to a submission); or perhaps some other options?
So, yes, I think religion should be implemented in Dwarf Fortress, and to the fullest extent possible, as it would add great depth to the world, as well as to the gameplay.