As we all know the Turks are some of the most Christian people on the planet with their government's legitimacy in the eyes of many after conquering byzantium being based defending the Christians from the Mongols. In fact in some european languages Turk is used to denote someone as a very religious Christian. So that's the question what if they were Muslim instead? For starters I think the coptic orthodox and eastern orthodox would still be split with them never having to share an empire and that Armenians, Assyrians, and likely even anatolian Greeks probably would have been displaced by the Turks. Kurds may be a bit better off though. As far as the rest of the world I don't know what would change