What Hungary do you have in mind sparticulous? During the second siege the ancestors of Arpad were still in or near what is today Ukraine and Pannonia at the time was ruled by the Avars / a century or so until the dissolution of the Avar Khaganate.The ummayyads cared more about money and commerce than they did for religious fanaticism. They would probably make the jewel of the world, Constantinople, their capital. When the Abbasid revolt did occur, the empire would probably split along the Roman and Persian lines rather than the abbassids being as successful in overtaking the entire empire except Spain. I could see the ummayads being more tolerant of alcohol use which would end up with a Muslim Russia. I would be surprised if Bulgaria and Hungary also didn’t become Muslim as well. So christemdom May be kept to the empire of Charlemagne borders and the British isles.
I see the ummayads seeing themselves as successors of the Roman Empire as controlling the east capital, Africa, and Spain, so they may seek to reunify the Roman Empire under the banner of the green moon. The dark age may be seen associated with Christianity and that religion may fade. Or since Islam still isn’t viewed as an entirely different faith, they would view Islam as the right path chosen by the Abrahamic god.