Historically the Middle East has been a fight between three major powers (Persia, Egypt and Asia Minor) AND local fights between local groups supported by one or more of those three powers. Until the Crusades, it was rare to have any outside power in the Middle East. Every so often one would attack Asia Minor, forcing Asia Minor to withdraw and upsetting the balance of power, but within a couple of hundred years Asia Minor would re enter, sometimes under a new tribal name (Thus the Hittites gave way to the Assyrians, who gave way to the Greeks, then the Romans, then the Greeks and then the Turks).
When Egypt was Christian, it spit with the Greeks Christians and remained a Separate Christian Church till the Crusades when the Mumaluks decided everyone in Egypt should be Moslem and started the prejudice against Christians in Egypt that exist to this day (The previous Shiite rulers of Egypt accepted the Christian Majority and lived with it, but it produced a very weak support for the Fatima Dynasty and lead to its replacement by a Sunni Kurdish Dynasty that in turn was replaced by the Mumaluks).
Turkish history since the Crusades is equally complex, the Turks were hired Mercenaries of the last of the Caliphs, but became a power themselves and settled in right is now Turkey (having come from what is know Turkestan). While the last of the Survivors of the Byzantine Empire fought the Turks, they also inter married with the Turks and as the Seljik Turks were replaced by the Ottoman Empire, the Ottoman Empire became more and more a Turkish AND Greek Empire as oppose to a pure Turkish empire (The legend of Osman, the founder of the Ottoman Turks shows this, he fought his Seljuk Turkish enemies and allied himself with a Greek Christian Nobleman who became the first of his advisers, many Turkish Noble Families stayed Christian till the 1600s when Islamic Fundamentalism swept threw Turkey and lead to "Reforms" that undid what Osman had set up and lead to a break up between the Greeks and The Turks that lead to Greek Independence in 1830 and today's Greek-Turkish hatred. The Greek-Turk hatred is more like a divorce where both sides blame the other then between two independent people).
Thus what happens in the Middle East has a Turkish component, but that also means Greek input for Turkey has to worry about both (in fact the main foreign Support for the Kurds for decades was the Greek Government). Thus while Greece is not presently in the calculation of anyone in the Middle East, it has been in the past and will be in the future.
In many ways, the Christians in the Middle East has tended to look to Turkey/Greece for support, except those that are tied in with Egypt, who tend to look to Egypt for support. The Shiite tend to seek support from Iran (as did the Jews in the Middle East prior to about 1850, when they shifted to France and Europe). Since the Crusades the Christians in the Lebanon has also looked to France for support, France giving them support even long after the end of the Crusades, i.e. into the 1600s and 1700s in addition to Napoleon's invasion of Egypt in 1795 (At the end of the Byzantine Empire, Venice had become a major supporter of the Empire, even through it had paid for the Fourth Crusade in 1204 that for all practical purposes had killed the Empire, Genoa supported the Turks, France supported the Empire at its fall in 1453, but Spain and England supported the Turks. Spain would turn against the Turks in the subsequent 100 years, while England would stay a loyal ally. so much for religion and alliances).
The Greek-Turkish relationship between 1204 (the Fall of Constantinople to the Fourth Crusades) and the 1830 War of Greek Independence had a huge affect on the Middle East. As long as both people saw each other as strong allies against the rest of the world, the Turkish Empire was strong and able to defeat anyone it wanted to defeat, including Turkey and Iran. On the other hand, once that internal alliance was destroyed in the 1600s, the Ottoman Empire became the Sick man of Europe
Just pointing out that this is more a fight between tribes then anything to do with religion, it is a continuance of tribal in fighting that goes back to ancient times.
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