It's good but I must point out that odds for the expelling of 20,000,000 non-Muslims are the same quite low since no such view exists in the Muslim world. Plus the modern Muslim insurgency was a direct product of exploitation during the Cold War, in places like Chechnya, Afghanistan, Iraq, Iran, and Lebanon mainly. You seem to portray Muslims as wanting to kill infidels for no ulterior motive, which strikes me as horribly stereotypical as a Muslim, but the Nazi Party and the KKK seem to be good comparisons to the UIR and the SoA.
Furthermore, how can you claim that Hulegu the Mongol is crushed in battle by the Egyptians? I can't imagine any realistic scenario where that happens. Furthermore, the Mamluks and Ottomans were Egyptian and Anatolian based Turkic dynasties with considerable military power; without the Mamluk factor in Egypt, I doubt they stood a chance against the Mongols. The Ottomans might have not risen here either, but they're worth a mention.
Oh, and one more thing. The Ommayyads as far as I know were reasonably more conservative than the Abbasids. And Omar ibn el Khattab was not an Ummayad; he was a Hashemite. Othman was an Omayyad, and even he did not start the "dynasty". It was more or less a republic till the assassination of the fourth caliph, Ali. Historians refer to that period as the "Rashidun" Caliphate, from the Arabic plural meaning "wise men" or "wise ones". The wise caliphs. The line goes like this: Abu Bakr, Omar, Uthman, and Ali. Then Muawiya and Ali engage in civil war, which Muawiya loses militarily but wins public support through propaganda. Ali is then assassinated by his own followers who believe the deception of Muawiya that Ali stepped down, deeming him a traitor. Muawiya is allowed to reign by Ali's son, the Hussein, only for him to name his son a successor before his death, sparking a second civil war which the Ummayid dynasty wins. I think Ali, Omar and Abu Bakr were Hashmites while Uthman and Muawiya were Ummayids. The Abbasids were Hashemites.
