With the idea at the top, I'd possibly go for pantheon alignment, rather than individual deity. (Provided they are grouped into pantheons).
This would then allow for followers of allied deities to get a bonus, and not force the can only help one group.
Example of this being in the party the Paladin is a follower of the God of War, and a Healer is a follower of the God of Healing, and the sailor is a follower of the God of the Sea. The three gods are allied in the same pantheon, so the party working together makes sense both from a practical approach and from the fact the gods get on.
Depends on the Pantheon, I guess - the Greek myth is full of gods playing very nasty tricks on people who just happened to favor another deity of the same pantheon. Because the Olympian gods were as much at odds with one another as they were allies.
I think the difference is what you're against. The ancient greeks only had one pantheon. Even the titans, and the primordial gods that came before them, were part of the same "order of things". The myth doesn't consider other pantheons because a pantheon defines the whole universe - if you consider *another* pantheon, you admit that your own is not complete. Other pantheons do not exist. The only rivalry, the only enmity, is *within* the pantheon.
Mortals have it easy: they are not gods, so they can just trade the words "faithful", "infidel", "unbeliever", and so on, which basically mean "those who know" and "those who are blind". But gods know : either a pantheon *is* the sum of the cosmos, or it isn't. Historical pantheons *were* the sum of the cosmos, so other gods did not exist. As such, they could not be enemies, and their followers were just idiots.
Monotheistic religions changed the game completely, because you cannot have enemies within (single deity, cannot be their own enemy). The enemy thus has to be without, and all religions need an enemy. But making an enemy of another god is acknowledging its existence in the cosmos - in essence, including it in the pantheon. This is what the christian faith did with Satan (create an enemy, integrate it in the cosmos, make it "lesser" and a rebel against the order of the One, but ultimately constrained by Fate as the One ordered). The other main adversary of the Christian faith, the Muslim faith, was different because *it is the same god* - the problem does not come from the god, but from the prophets and the holy doctrine. It's a kind of very successful heresy
I think creating a pantheon needs to take that into account : you cannot create two pantheons and say they are enemies. The *people* might be enemies, but either it is a single pantheon, or they are the same gods with different names, and the problem comes from the people, not from the gods.
The consequence is, segregating *by pantheon* does not work because it is self-defeating: admitting the existence of the "other" gods makes them part of the pantheon (litterally "everything that is divine"). Either it is a schism in the faith (same god, different doctrines), or it is a rivalry within the pantheon itself.
For a pantheon with many gods, the second case is much easier to set up (just watch the Olympian Gods). For a pantheon with few gods (or a monotheistic religion), the first choice is much more obvious.