SCHISMS
When comparing the Civ series to real history, one of the weakest points is the lack of religious schisms. For example, one of the more brutal wars in European history was the 30 years war, which killed off about a third of the population of Germany and was a struggle between catholics and protestants, with neighbouring countries like France, Sweden and Austria and others interfering in this powerstruggle. However, in in the game, in that era all the participants of the 30 year war would be "Christian" and probably big buddies due to the same religion diplomatic modifier. Similar tensions exist in Islam with the Sunni vs Shia schism.
RELIGIOUS TENSION.
There are countless examples of civil wars caused by differences in religion in the world today or in history. You could frame the tension in Northern Ireland as a struggle between Protestants and Catholics, or you could frame it as an ethnic struggle between the majority of British settlers and a minority of native Irish. You can frame the recent Sri Lanka civil war as a struggle between Hindus and Buddhists, or a struggle of (predominantly Hindu) Tamil ethnic group versus the Buddhist Sinhalese. You could see the Yugoslav civil war as an ethnic war between Croats, Serbs and Bosniaks, or as a religious war between Catholics, Orthodox and muslims.
However you can't just roll etnicity, culture and religion together into a group identity, and let the different religions in a city represent ethnic minorities (although in the case of diaspora Judaism that would certainly be a good model) as religions tend to jump from civilization to civilization and matching state religion with your neighbouring civ is an important diplomatic tool in the game. A religion (or schism of a religion) is a group in its own right.
For example, a few years ago the Iraqi police found a big pile of corpses stashed away in an alley. Upon identifying the victims, they found that most of them had the same first name: Omar. Weird? Creepy? Yes, until you remember there is a continual civil war going on in Iraq between Sunnis and Shias. Iraqis in the same area often share the same language and ethnicity. So it is hard to distinguish between Sunnis and Shias if a person wants to hide his religious affiliation. However, "Omar" is a typical Sunni name so Shia death squads probably just rounded up everybody with that name (possibly by the phone book) and murdered them. The Sunni Islamic State (IS) gets all the bad press lately but the Shias in Iraq aren't all sweetness and light either.
So if the ambition is to make C2C historically accurate, there should be a mechanism to create schism religions. I propose that a schism can be created if a religion is present in a civ but that civ does not have the holy city. The civ must also have researched the tech that started the religion. It would also require spending a Great Prophet. The religion then splits into two new religions: the orthodox version and the new version. The name of the schism can be taken from a historical list, or named after the Great Prophet who started the schism: Luther starts Lutherian Christianity. Every follower of the religion in the civ that founds the schism converts to that schism while everybody outside stays the same, although the original religion gets renamed to Orthodox [religion]. Both religions then continue to spread, also into each other's territories.
For example, Christianity started in the Roman Empire with Jerusalem as the holy city. Later the Roman Empire split in an Eastern and a Western Roman Empire. The Eastern part retained Jerusalem and became Orthodox Christian, the Western part became Catholic Christian with Rome as its new holy city. Catholicism spread through Western Europe until people like Luther and Calvin (Great Prophets) created Lutherian and Calvinist Christianity. Mormonism should also be a schism.
In the case of Islam, the Shia schism is most prevalent in the Persian (Iranian) area.
To mimick this in the game, lets say that Islam started in Arabia, with Mecca as its holy city. Islam spread to the Persian Empire (called Sassanid Empire at that time). The Persians then started the Shia schism. The Arabs then conquered Persia but the schism has already happenened and creates troubles until this day. This is not exactly how the Shia religion started historically, but it mimicks the final results.
But why would a player start a schism? I think the game rules should be adapted so that NOT having the Holy City is a big disadvantage. For example, right now having the Holy City gives you +1 gold per city it has followers in. If the rules are changed so that the Holy City gives +2 gold per city with followers, but the city with followers get -1 gold, it would not cost the owner of the Holy City more, but it would transfer money from other civs to the owner of the Holy city. Additional Espionage points can be given to the owner of the Holy City for every city with followers outside the owning civ. Also if you own the Holy City, you could get a combat bonus for attacking any enemy city with your followers in it (who act as fifth-columnists).
This however would mean the number of religions in the game would grow even larger. So there should also be a mechanism to get rid of obsolete religions. The 30 year war was fought between Catholic Christians, Lutherian Christians, and calvinist Christians, not Asatru, Kemetism and Hellenism followers. This can be done by simple slowly competing away of older religions by newer religions, or it can be tied in with the Revolutions mod. The last makes religion a double-edged sword instead of the always-positive as it is now. More religions means you can stack the bonuses from the various temples and cathedrals but also creates increased religious tension which if not sufficiently handled can cause religious revolts or even religious civil wars. The result of such religious revolts could be the massacre or expulsion of the followers of a religion, and/or the destruction of its religious buildings. A recent example of this is the destruction of the Babri Masjid mosque in India in 1992 by Hindu mobs because the Hindus claim the mosque was built on Hindu holy ground.
http://en.wikipedia.org/wiki/Demolition_of_the_Babri_Masjid
This set off a number of follow-up riots in India and neighbouring countries leading to much death and destruction.
Which religion gets expelled (if any) should be random but influenced by competition strength which depends on several factors, like the age of the religion (newer religions compete stronger) and whether the religion is state religion.
There is an overwhelming number of examples that show that multiple religions within the same city can lead to tension, both historical and today. While some analysts say that the Middle East is on the brink of a large war between Sunnis and Shias with Sunni countries bombing the Jemen Houthi Shia tribe, South Asia continues to have tensions between hindus, muslims and Buddhists: the latest news today is about muslim Rohingya people fleeing Burma by boats due to "discrimination" by their Buddhists neighbours (*) ). Even in Western Europe, which has had a long period of stability after World War 2, tensions are growing, with thousands of Europeans demonstrating against the "islamization" of their countries due to open borders policy (google PEGIDA).
(*)
http://en.wikipedia.org/wiki/2012_Rakhine_State_riots
Dancing Hoskuld stated a while back that polytheist religions tend to be more tolerant. After some google-research I concluded that he was right in that polytheist religions tend to be friendly towards other polytheist religions, sometimes even adopting each other's gods. The same can not be said about the relation between polytheist religions and non-polytheist religions, or non-polytheist religions among each other, with monotheist religions perhaps being the most intolerant towards competition. So perhaps the religions should be divided in groups:
-nature/spirit religions (e.g. Shamanism, Voodoo)
-polytheist religions (e.g. Asatru, Hellenism, Hinduism, Kemetism)
-monotheist religions (e.g. Zoroastrianism, Christianity, Judaism, Islam)
-philosophical religions (e.g. Taoism, Confucianism, Scientology)
(I'm not sure where to put Buddhism; although Buddha said he was only a man, which makes Buddhism a philosophical religion, many Buddhists worship Buddha as a god, making it similar to monotheism).
So polytheist religions should tolerate each other, but after that, cities should suffer a religious tension malus on their Revolutions bar which grows exponentially with the number of religions (or schisms of religions) present in the city. This malus should be highly dependent on difficulty level.
This system would present players with an interesting choice: collect several religions and stack the sweet bonuses from the various temples, but at the risk of civil war, or act like the Tokugawa Shogunate did, who closed off Japan completely from outsiders because of fears that Christianity would destabilize Japan.
It would also make missionaries weapons to destabilize your neighbouring civs, much like how Saudi Arabia spends vast amounts of money to spread Sunni Islam around the world.
One last idea: religions should have a current focus, something that is preached predominantly in the temples. Christianity has gone through pacifist and warlike phases, through intolerant and tolerant phases, through periods of ascetism and strict morality, and periods of commercialism (selling indulgences). Islam has had its openminded and narrowminded phases. So whichever civ owns the Holy City of a religion (or its schism) can decide what is being preached in the temples, and so choose the bonus his empire needs most. Civs who don't have the Holy City of their religion don't get to choose but simply get what the owner of the Holy City decided. Which may be another reason to start a schism. For example, preaching Commercial (like temple prostitution or selling indulgences) would increase the money flow towards the Holy City. But I'll leave the details for a later post.