Well, to clear up some misconceptions, Greece only became nearly entirely Christian and Anatolia became only nearly entirely Muslim in 1923-1924, whereupon mutually agreed upon population transfers exchanged the many Christian populations in Anatolia, particularly on the coast, with many Muslim populations, particularly in the North of Greece. This also happened throughout the Balkans with many Muslim populations moving back to Anatolia.

Also, keep in mind that in the Ottoman Empire while conversion often took place for a variety of reasons, many peasant populations remained Christian and went relatively unmolested within the Empire, and in its later years the Byzantine Empire had been concentrated in Greece and Western Anatolia, whereas Eastern and Central Anatolia had been conquered by the Muslim Turks many centuries prior, which helped to solidify the divide which was already present to some degree previously in Anatolia, between the Western and Coastal populations which were more throughly linked with Constantinople and the more independent populations further inland.

After a catastrophic defeat at the Siege of Vienna in 1683, the Ottomans were forced to sign the Treaty of Karlowitz in 1699. Per the terms of the treaty, the Ottomans ceded a massive portion of modern-day Hungary, Bosnia and Herzegovina, Croatia, and Slovenia. The treaty marked the end of significant Ottoman expansion in Europe, and presaged a series of wars over the next century and a half that left the Ottoman lands in Europe ravaged.

Several powers played up nationalist sentiments among the many predominantly Christian non-Turkish ethnic groups in the Balkans and Ukraine by claiming to act as defenders of particular religious or national groups. As Christian borders advanced towards Anatolia during this time after Ottoman defeats, Muslims fled towards the Turkish center.

Pressure from the British Empire, France, and the Russian Empire to make substantial political, economic, and social reforms under the threat of partition led to instability amongst Ottoman subjects, with several rebellions sparking bloodshed against Christians that remained Ottoman subjects. The communities that survived or were relatively untouched by these events nonetheless began to migrate in ever larger numbers to the lands of their co-religionists.

Finkel, Caroline (2005). Osman's Dream: The History of The Ottoman Empire.