I think it would be too overt to have a game strictly about Christianity or a major faith; the problem with that is we already have opinions on Christianity and its history, so it sort of restricts the ability of the game to tell a proper story. Players will have decided who the good guys and bad guys are before the game could even present them.
In terms of a religion based RPG (4X / Empire building games can do religion in a non-biased way, but RPGs are more personal), I'm have trouble imagining it. You could have a game centered around historical events, but a lot of famous historical events are pretty black and white (Inquisition = bad, Crusades = bad).
I only have one idea for a game that really offers moral choice in terms of accepting or rejecting the religious side of the story:
You could be a missionary in a European imperial colony, say, late 1800s/early 1900s China. You arrive with high ideals, wanting to spread the Good Word to the native Chinese as well as help educate / modernize them. Your fellow missionaries are for the most part legitimately interested in helping the locals. However, you also realize that you are somewhat a tool of European foreign policy, an instrument of "soft power" meant to bring the natives under the influence of the colonial powers and away from the authority of the Chinese government. Benefiting from the weakness of the Chinese throne, missionaries and their British / American political backers demand (and receive) special authority in China, giving them what many believe to be undeserved privilege and power above the law. Meanwhile, there is growing resentment in some circles against your missionary work, in part because it diminishes the autonomy of the Chinese government, in part because they are seen as an extension of unwelcome foreign powers pushing their unwelcome religion onto the people. You are aware that this resentment is in danger of boiling over into open violence against yourself and your fellow missionaries, and the colonial troops in the area will not be enough to contain the violence if it erupts. I guess the endings could be:
1. Your character abandons the mission, having become disenchanted by the nasty politics surrounding the missionary movement.
2. Your character sticks with the mission, but flees when the violent uprising begins, abandoning his fellow missionaries and their converts to the wrath of the rebels.
3. Your character sticks with the mission and faces whatever comes...
It'd sort of be a moral question of the right of missionaries to do their work in foreign nations when half the population welcomes them and the other half wants them gone, with a sort of "dirty means to a righteous end" question regarding using your nation's imperial influence to force the native government to accept the missionaries.
The only problem really is the gameplay...clearly the gameplay could not actually be related to the day to day life of being a missionary, because that's really boring. Maybe you could be some kind of missionary archaeologist going throw ancient Chinese tombs or something, I dunno.
