Well actually they didn't hate the muslims they just did what every other emipre would have done ally with someone and destroy the biggest threat for your expansion here being the Muslims. I read that most of the Muslim cities destryed by the mongols was because they "rebelled" not sending tribute to them so then the khans came from the steeps entered killed burned etc. Making As anyother Emipre would do to subjugate the population faster.
To my experience they will ally if they have a common fow or have no land border, If whichever factions attacks an other and has no land border the AI will automatically ask for peace even if it was the one that started the invasion. Try it yourself and offer ceasefire it will be very generous for according to the AI standards.
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