I think the treatment of Bloodless Xristos is really interesting, and I'm wrestling with it. Various distinct differences between the game's treatment and historical Christianity jump out, and seem worth mentioning.
Most strikingly, there is no Papal Rome. There is no Bishop of Xristos who is a claimant to the throne of the Empire of Eagles, transmuted from a worldly to a celestial reign. It's not clear that the Empire of Eagles ever converted en masse to the religion of Xristos, and persecuted followers of the Gods of the Empire of Eagles with its imperial might. It's not clear that there was ever (and it's sort of implied that there wasn't ever) a fusion of the imperial values of hierarchy, control, and expansion with the monastic and utopian values of the followers of Xristos. One would not expect, from the short description here, monasteries of Bloodless Xristos functioning as an intact network of trade and information, directed from an imperial center, in a hierarchy of control. One would not expect priests reporting to bishops reporting to monsignors reporting to cardinals. There seems to be disagreement among followers of Xristos, but no ecumenical councils banning heretics.
Secondly, Xristos seems to have sprung from nowhere -- neither from the Old Gods, nor from the Gods of the Empire of Eagles, but also not from any rebellious province with its own pre-existing monotheism. Xristos begins life by creating the world -- as opposed to being initially a man, claimed as a king of a specific people, elevated to Godhood, and then awkwardly merged with a pre-existing world-creator God who already had a name. There is therefore not the embarrassment of a competing, older group, using the same books, offering the same narrative of world-creation, but scorning Xristos as a fanciful addition to the canon. The followers of Xristos are spared the misfortune of having to condemn these folks -- who would, if they existed, be found in all walks of life, but among other things as wealthy owners of villas, claiming the right to legal proceedings under the Law of the Empire of Eagles and owning slaves who are followers of Xristos -- as quasi-demonic outcasts eternally cursed for having spurned their Redeemer. The followers of Xristos need not petition kings and lords, demanding that these embarrassing predecessors be deprived of their slaves and holdings, forbidden from preaching, dispersed and banished.
There were also, as far as we know, no massively popular Mystery Religions competing with the familial and human gods of the Empire of Eagles; the legionnaires of the Eagles, unlike those of Rome, were not swayed en masse by the cults of Isis or Mithra.
So Xristos gets to be the only holistic, ineffable, mystical god, without having to appropriate anything from anyone, or claim to fulfill any particularistic prophecies of rebellious provinces. He is Logos, world-creator, without any awkward familial relationship to a pre-existing father-god who might be Himself, somehow. His followers never merged with empire, have no single Holy Father commanding them, no hierarchy, and no elder-sibling competitors to persecute
So if the followers of Xristos gain dominion over the land -- if, over the course of the next few hundred years, they come to almost fully displace the Old Gods and the Gods of the Empire of Eagles -- there doesn't seem to be that much to worry about, does there?. They are unlikely to wage war on heretics (since they are so benignly multifarous) or elder siblings(since they don't have any), or engage in pogroms and crusades. They really do hold peace, healing, mercy, penitence, and humility to be the greatest virtues... in deeds as well as words. I guess we should be rooting for them, then.
Lucky Xristos!
As a first approximation of the English or Danish Dark Ages, erasing the Pope and the Jews does not cause tremendous historical problems. (It's much more of a distortion if dealing with, say, Merovignian France, or southern Germany.)
Still, it's an interesting choice. Xristos and his followers are sort of what Christianity -- especially a low-church Protestant Christianity -- would like to imagine that it was in the Dark Ages. As opposed to what it actually was. It's an idealized version.
Which is a political choice. One which, as a Jew, I'm a little uncomfortable with. That may be my baggage, of course.