The populace does in fact remain Muslim-with a big caveat that a considerable part had converted earlier when Michael and Nikepheros were screwing around in the region, and the region does have a non trivial number of Assyrians. That being said, the Turks remain muslim except for the very top leadership that got a little wet courtesy a priest. The understanding here (courtesy Leo and Andreas Makedon) is that the Empire is accepting of muslims, and they can go back to doing whatever they were doing once the Latin zeal dies down, provided they remain loyal. Of course Leo is not a completely uncharismatic figure, and his conversion is genuine-so he could potentially sway some of the nobles to the cross for real, long term. At the moment it is all superficial-a mummers farce which the Latins are being fed. The Persian Turks of course remain committed to Islam, and there will be quite a major clusterfuck regarding this down the road. Without going too much into details, the tensions between the two faiths for the Turks will lead to a rather major crisis of TTL 20th Century....So the Turkish lords convert, but I imagine the populace remains Muslim, no? And the Turks east of the Zagros still remain Muslim, and still with the fervor of the newly converted. That is bound to have interesting repercussions...
Also, how much of an opposition did George face within the Church regarding the Crusade? Replacing a patriarch and a host of bishops on a theological issue where theological opinion has been pretty definite for over a century (IIRC, Nikephoros Phokas tried to have the soldiers fallen against the Muslims canonized, but the Patriarch was vehemently opposed) is the best way to create a mini-schism within the Church, particularly if Theodore is long-serving and well regarded (and stubborn). Of course, nothing succeeds like success (battlefield victories can easily be transformed into divine sanction), and much depends on the justification of the Patriarch's dismissal, but unless reconciled at some point, I wouldn't be surprised if this was the beginning of a pietistic/pacifistic movement with religious and social overtones, that could merge with alt-Bogomilism or go its own way. Contrary to popular belief, the Byzantine emperors did not always get their way with the Church.
So the theological issue is not quite settled. Phokas may have failed to get canonizations done (the POD is from that period, and I see no reason to change it), but John and Basil had effectively encouraged communal tension in the Levant (and in Basil's case, exploited it to conquer the region-see the update titled Tale of Two Emperors, War in the East). The Orphans for instance where first conceived out of kids, well-orphaned by that war and interfaith riots. The Aegean elite of course had lost very little there and their attitudes have not changed directly. Those of Levantine Melkite extraction on the other hand have a much more hardline stance (see the story about Paul and Peter above) and some have indeed risen to high office (Paul did end his career as Patriarch of Antioch). This is not to say the Greek Orthodox opinion is pro-Crusade, but it is more divided than OTL (I'd say 65% opposed to 35% for it) and certainly not extremely opposed.
There is also the matter of the two Basils having converted the Patriarchate to an effective bureaucratic (as opposed to ecclesiastical) position. Well, they were hardly the first to do it but they filled the ranks with retired bureaucrats to manage the population transfers to Egypt (distribute tokens to faithful), hellenize masses (schools for Greek) and other welfare means. This is not to mean there are no real men of cloth left or respected, but the church is far more a government organ than, say OTL (no one is going to pull a Kerularious grade stunt and expect their eyes to last the week). The non-governmental men in fact are more in frontier territories and are more likely to be hardliners than the coastal elite
Theodore was another bureaucrat John II had appointed in 1070, and so he did not quite have the connections to create opposition (nor was he willing to push it beyond a point-he was sufficiently loyal to John II not rubber-stamp a reversal of stance but not to the point of gambling with his families life). The bureaucrats mostly fell in line and were replaced, really recalcitrant bishops with deep roots were quietly given dressing downs by sympathetic superiors and those with a shaky position are always replaceable. Your point about a new movement merging with neo-Bogomilism is however very much along the right direction-there will be people who will be starting to question this war (especially if things go south-they can't do much if Turks suddenly find Christ before a battle) and seek out like minds, who may or may not be more sympathetic to heresies in general. Ultimately, the conditions of 11th Century Byzantium TTL are fertile ground for new theological ideas, which could have interesting repercussions further down the road. Who in 100 CE would have thought a Jewish sect would make it so big in another 300 years?
Idk if anyone will think the end to be bittersweet. Interconfessional middle eastern wars are messy...... But yes, things will be getting worse soon.Ah crap, this is going to start bad, go worse and end bittersweet.