So, I have been rethinking this rather important part of the TL for a while, in the light of the discussion here.
DIfferently from my previous assumptions on the issue, I can understand and accept the arguments that a radical reChristianization of conquered North Africa and the Middle East a la Reconquista is likely unfeasible (even if I really see no valid reason why Iberia itself should not be reChristianized as radically as IOTL), even if an European conquest would stop ongoing deChristianization of the region, and thus keep it much more religiously mixed than IOTL. If European conquest of the area wants to endure, it would need to adopt some amount of pragmatic de facto tolerance. OTOH, if European conquerors are going to give up such radical assimilation efforts in order to make their rule more manageable, they are also going to be much more tolerant of doctrinal differences with local Christian communities.
I remain however far more skeptical of why TTL European powers should find it so difficult to conquer the Near East and stabilize their rule there, esp. if they eventually give up radical assimilation.
First, I am rather skeptical that 15th century Europe really still suffered a significant technological gap with the Muslim world IOTL, and even if it did, surely TTL developments (stronger political stability fostering early rise of trade-based urban society) is going to wholly wipe it out much earlier than OTL.
Second, I cannot understand why invading 15th century European powers should be radically unable to develop an effective mutually-beneficial alliance and division of turfs across the Muslim world. Some amount of relatively minor squabbles, occasionally exploding into armed conflicts, are indeed likely and perhaps inevitable, but radical estrangement exploding in total war and wrecking their conquest effort is a possible outcome but not mandated by any means. Certainly 16th century powers were able to achieve such a largely effective division of spheres of influence about colonization of the Americas, and the political differences with the previous century were minor. And papal authority about this was an unnecessary figleaf, the powers mostly stuck to the proposed division because it seemed a sensible compromise, 16th century monarchs were totally able to ignore papal authority when it messed with their vital interests, Canossa was dead and buried. So it does not really seem necessary ITTL to coordinate a new Crusade, secular diplomacy can do it on its own as necessary.
Third, the economic-demographic balance of power and resource committment for TTL 15th century Europe and the Muslim world does not really seem to make an Euro conquest so unlikely, if the Euro powers temporarily make a coherent effort. Let's not forget that the Muslim world would lack some rather significant assets ITTL, Anatolia was never lost by the Byzantines and the Reconquista was done much earlier, and the Euro powers would have a much larger power base than IOTL back home. Even if European encroachment would pull Islam back closer to political unity into an ATL equivalent of an Ottoman Empire spanning the Near East, it is still feasible for an Euro parallel invasion, if not quite possibly outright alliance, to crush it militarly.
Granted that the success of Euro conquest of the Near East requires the Euro powers keeping a functional alliance of convenience, and this is by no means granted, but neither any impossible either, I still have to see a really convincing argument why the 15th century Near East would be so awesome that such an Euro conquest of it was so implausible with TTL optimized 15th century Europe.
