rogue131
Byzantine Historian
The Western and Eastern Churches were at loggerheads since well before the Great Schism. Having Byzantium start off as Orthodox isn't strictly accurate but it's better than adding yet more iron fisted determinism later in the game.
Right on point, the East and West had been drifting apart for a great deal of the later Roman imperial history. Diocletian's division of the Empire, and Constantine's founding of Constantinople only made this divide a more permanent and visible reality. Remember Basil I had angered the Pope by cleverly convincing Bulgaria to follow the See of Constantinople over Rome, by "excluding Rome and Constantinople from advising the Bulgarians and referring the question to the other Patriarchates...which were consequently in the East.

You could do what Rhye has done in RFC:Europe, have The Great Schism impose an immediate diplomatic penalty between Orthodoxy and Catholicism.