So, first of all, there are infinite possibilities of alt history scenarios, this post doesn't require to write a scenario, just to think of how could it develop
This scenario also means that many butterflies will be slaughtered, sorry :S
Well, it all started when I readed this TL, that run between 1066 and 194-something, and something interesting is that while Russia became independent and almost as strong as OTL, the byzantine empire replaced the Russian empire as the main orthodox country, here is a map of the world by 1850:
At this time, the byzantine empire was a centralized absolute monarchy, with the orthodoxy being the state religion, had a population of about 160 million people and was hellenizing his territories, just like Russia russificate them
but in the following years, during a war against germany and other states the byzantine state fell into civil war and turned into the communist union of rome:
It is the Red state on italy, balkans, Persia and Anatolia
What do you think? Would it possible for the byzantines to end like the Russians?