To my understanding, this was only in Athens. Outlying regions would have different focuses for gods they preferred & local worship practices. You were expected to adhere to Athens' religious standards when interacting with Athens (for the Olympics, as you mentioned), but other areas did their own thing when they didn't need to directly bother dealing with Athens. As I said though, I'm not a religious scholar, so I may be mistaken on that.
The Olympics were not an Athenian thing. After all it was in Peloponnese, a land mass that was under the political dominance of Sparta.
The Olympics were a festival dedicated to Greece (as a nation of peoples not a state) and the Greek gods. It reminded the diverse city states (including their colonies) the things they had in common:
Language, Heritage/bloodline, Religious beliefs and their common destiny: That one day they will uplift the barbarians (Πας μη έλλην βάρβαρος = Non Greek equals barbarian) of the rest of the world to an equal cultural and educational state ( I can only dream of how they felt when word of Alexanders success in Persian was resounding thought the Greek mainland).
The Greek Pantheon was diverse, there were 12 main gods but if you count in the vassals, lesser powers, spirits, daemons and mythical creatures and some times even mortals that ascended to demigod status (To use your example of Athens, its almost mythic founder Theseus) you could indeed pretty much loose it. However all those were ingrained in the Dodekatheon and thereby fulfilled the criterion of 'Greek religion'.
OFC if you interacted with an Athenian you would be informed that Athena and Theseus were prominent figures of their worship. An islander would pay service to Poseidon, in Corinth (famous for its holy prostitution at the time) the devotion to Aphrodite was paramount. But all of them accepted and paid service (even token at sometimes) to the whole Pantheon.
An Athenian woman would pay her respects both to Hera (goddess of marriage and household among others) and to Athena the patron of the city, and during a visit to say Iolkos would pass by the temple of Poseidon to pay her respects. Similarly her husband would do the above, and while on war would pray to Ares and during peacetime since he is say a blacksmith to Hephaestus. And I dont want to take into account the cults that had to do with orgies and necromancy....
Sorry for derailing.
Otherwise, they use pantheons for ancient religions. Hence why Greece is Eastern Orthodox.
Well yes, but the real reason that they use Eastern Orthodox is because the system is messed up. To take Greece as an example, they use the Ancient Greeks as the CiV but they use the modern Greeks for religion. Same with Aztecs for example. On the other hand since there is an appropriate religion for Persia to follow on the time the CiV is represented (Aechmanids) and not modern day Iran, is the reason they don't choose Islam.
Hm. True, I could see some of those as religions, or religion-like. The issue is, again, how do you represent such a diverse set of faiths?
With the new reformation system ill use Christianity as an example not with bias but with virtue of knowledge, I dont want to post errors since I am not that versed in NA religions. They could have added 'core' religions (the old ones plus some new to encompass all civs in the game) and once you choose the reformation policy instead of choosing a new belief bluntly, you could choose said belief and be given a new set of Icons and a renaming tag (obviously there should have been scripted choices for the AI), thus after the reformation your 'Christianity' would be reformed to Orthodoxy or Catholicism and the NA (dont know names sorry) religion could be named the ghost dance (as you people post it
) for say the Iroquois and the Shoshone could name it something else.
