Yes, that was a factor, although I do not agree with those who theorize that it was the main factor. There was also the earlier war with Persia, which weakened both Byzantium and the Persians and helped open the way to the Turks. And there was the admittedly two-sided cultural war that had gone on for many hundreds of years between the Orthodox and Catholic Churches.
The popes tried desperately for many years to persuade Venice, France, Naples, Genoa, Spain, and the other powers of the time to come to the rescue of Christendom against the Turkish threat. In vain, because they were all too busy fighting each other, especially the French and the Holy Roman Emperor.
That Crusade which you mention went astray, but the other crusades did not, and would have helped the Byzantines, if they had only been willing to cooperate better with the Christian west.
There is plenty of blame to go around, certainly. If Europe had stood together, the Muslim threat never would have gotten as far as it did.
I don’t know about that. Especially as the Church of Rome (and the West) became ascendant, they made more and more demands of the Orthodox in return for their military aid. If there was one thing that the average Roman (I’ll use the proper term instead of the all too common “Byzantine”) was mostly unwilling to compromise on, it was his faith. Of course, even with the Council of Florence, the West didn’t really snap to the Empire’s defense.
I agree about the war with Persia that left both empires worn down and allowed the muslimes to assert themselves in the ME. It’s like two heavyweights beat each other to a pulp and then some pipsqueak delivers the coup de grace—completely absorbing one and mauling the other.