Here's a thought, and a potential monkey wrench -- what kind of effect would a Scientific (as well as Agricultural/Economic) Revolution(s) have in, say, Al-Andus have on Catholic Europe and the ERE?
In the ERE, not much I think, but I am not very knowledgeable about that. In Europe, well consequences would be enormous.
Culture-wise, if Aristotelianism is challenged in the Andalusian twelfth century, it won't make it to Europe. Forget St. Thomas and all that. However, it may work both ways, favoring more independent lines of thinking OR killing European science in the cradle. The main lines of European Scolasticism would probably be closer to Ockham's philosophy than Thomas' in the end.
By the way, Roger Bacon's plans may find a more favorable audience in a Christian Europe that lags behind the Muslims tech-wise and knows it. Some innovations may spread earlier and quicker (windmills and watermills).
Oh, and clocks I guess. Clocks are all-important for both Muslims and Christians.
Other than than, probably the most audacious Andalusian ideas will be labeled as heretical, as it actually happened with OTL's Averroism.
Of course, the politics of Iberian Peninsula are completely changed, but the Christian Kingdoms are still there, though probably different than OTL. My guess is European science and tech lags behind for a while, then recovers more quickly respect to OTL. In any case, West and Islam were
heavily interrelated at the time, though in the Muslim perspective there West was barely worth noticing when some crusader appeared.
The Toledo school won't exist TTL, but the need for the translation would still be there and the clerics who did them would operate. Only, different texts are translated. Instead of commentaries of Aristotle,
critiques of Aristotle. The Church might get along with that, if that stuff is not too openly Muslim. After all, the Greek philosophers were PAGANS. I doubt, however, that a "copernican" cosmology would be welcomed. The attractive of Aristotelian metaphysics for the needs of the Abrahamic religions is rather apparent, and Christianity might also find itself on the side of conservatorism, especially if the Eastern christians provide knowledge of the greek texts...
Oh, and you'd probably have an amazing development of linguistics in the West.