HOLY SMOKE.
What were the Crusades really about?

Quote:

But there was another call to arms: Alexius I Comnenus, the emperor of Byzantium—that is, of Catholic Europe’s Eastern brother—had asked the Pope for help against Muslim forces threatening his borders. Again, however, this was something less than an emergency. Byzantium and Islam did fight, but no more frequently than most neighboring powers of the time.

No, this call wasn´t "business as usual". Ten years before Alexios became emperor in 1081, the Byzantine forces lost to the Turkish Seljuks - rather new actors in the area, having taken control of what is now Iraq only in 1055 - in the battle of Manzikert in 1071, after which Anatolya, the heart of the Empire, was never again to be truly under the rule of Byzantine Empire (alias Eastern Roman Empire) - who had just, in 1061, lost their last possessions in Italy to another group of aggressive newcomers, the Normans. It was one of the defining moments in the history of the Empire - after the Muslim forces had gained a foothold in Anatolya, they never left. The most important and the which doomed the Empire was the sacking of Constantinople and the establishment of the Latin Empire(1204-1261). One of the states that gained from this was the Seljuk Sultanate of Rûm(Rome) in eastern Anatolya(the main Seljuk state was already in deep decline).

Most of these territories were under the jurisdiction of the Byzantine Empire and hence of the Greek Orthodox Church, which, to Rome’s abiding fury, had broken with the Western Church in 1054.

The two branches of Christianity broke apart from each other in 1054, after drifting away from each other for centuries - for example, the last eastern popes ruled in the 8th century(before that, popes from Asia Minor, Greece or North Africa were quite common).