I suspect you could make a very solid argument that the Japanese involvement in the WWII carried significant religious overtones with their prevalent form of Buddhism.
Japan has a unique mix of martial spirit, a hold-over from Shintoism, and delicate pacifist appreciation for beauty and gentle things, an influence from Buddhism. The balance of the two is Zen. Wars initiated by Japanese leaders have nearly always been on political or economic motivation, though, not religious.
Lots of racial, economic, ideological, and cultural stuff mixed up in there as well of course. Anyway, I'm sure there are other examples. Pick any religion thats been around for a while(amish excluded), and we could probably point out some sort of religious strife initiated by its followers.
Which brings me to my suggestions for CivV:
Religions:
1. There would be several religious techs. The first Civ to gain the tech picks up an appropriate religion. For example if the Greeks snag polytheism, they get the greek pantheon, if the Indians hit it they get Hinduism and so forth. The 2nd Civ to get the tech creates a schism. The schism is a branch of the original religion founded by the the 1st Civ. So if your 1st to theology you get Catholicism, the next guy to hit theology gets Orthodoxy. This will complicate diplomacy, and will also keep 1 player from founding all the religions. Civs on different side of the split would be able to get along unless one of the two or both had theocracy, at which point its time to kill some heretics.
I like the concept of national unique historically-accurate religions. Some ideas:
Brennus: Druidry
Ragnar: Asatru
Elizabeth and Churchill: Church of England
Julius and Augustus: Roman Paganism (early) and Roman Catholicism (late)
Alexander: Greek Paganism (early) and Greek Orthodox (late)
Hatshepsut and Ramesses II: Egyptian Paganism (early) and Gnostic Christianity (late)
Saladin: Arab Paganism (early) and Islam (late)
Catherine, Peter, and Stalin: Slavic Paganism (early), Russian Orthodox (late)
...and so on.
To balance out the influence of multiple religions, when a later shrine is founded, it should obsolete the earlier shrine.
For Stalin, I know his regime was State Atheism, but that should be a religion civic, currently absent in the game: it's not "free religion" because no religion was allowed, and it's not "paganism" either. A State Atheism civic should add +1 hammer to workshops and mines, +1 food to farms, nullify any shrine gold revenue, nullify the happy effects of religious buildings, but also at the same time convert any unhappy citizens to basic "citizen" specialists, of just 1 hammer and no GPP. High upkeep (due to having to infuse the population with propaganda, keep the Secret Police busy arresting underground religious groups, etc.)
For the American leaders, let the early religion be "Folk Traditions" and the late religion be "Televangelism". It would be an abstraction of what religion essentially was and is, in America, rather than a specifically historic single religion.
Most early religion discoveries should happen with "Polytheism". Most late religion discoveries should happen with "Theology".
2. I'd find a place for a military column in civics.
I drive myself crazy every time I try to think of a way to improve how civics line up. The dimensions to civics in the present civ4 don't seem "quite right", but then neither have been any of the ideas I've come up with. At some point one dimension always has effects on another that can seem to get properly captured.
My latest flawed attempt has been:
1) Governmental Succession
a. Interpersonal Combat
b. Factional Struggle
c. Inheritance
d. Republican Appointment
e. Representative Election
f. Direct Election
2) Domestic Security Policy
a. Kill dissidents (Despotism)
b. Imprison dissidents (Police State)
c. Harrass dissidents (Propaganda)
d. Tolerate dissidents (Free Speech)
e. Encourage dissidents (Sensationalist Journalism)
3) Domestic Economic Policy
a. Personal command labor
b. Specialized labor (allows slave-whipping, specialists)
c. Caste System
d. Capitalism
e. Unionization
f. Central Planning
g. Syndicalism
4) Trade Policy
a. Ad hoc trades
b. Trade by treaty
c. Merchant explorers
d. Mercantilism
e. Protected markets
f. Free markets
5) Religious Policy
a. Shamanism (no state religion)
b. Priestcraft (organized religion)
c. Theocracy
d. State Atheism (described up above)
e. Religious tolerance
6) Military Policy
a. Random Warriors
b. Warrior Caste (+2 XP)
c. Professional Voluntary Soldiery (+25% unit production)
d. National Service (can draft)
Changes to trade policy should never spark "anarchy". That's ridiculous, and never was there such in history. The others should be a percentage chance of anarchy, modified lower for spiritual leaders, but never impossible.
I toss these around too often to really stand behind them 100% though. It's frustrating.