Anatolia was ruled by Turkic states by far longer but it still wasn't homogenous. There were Turkish majority places in modern day Greece and Greek majority places in modern day Turkey. After Greek rebellions and Balkan wars the two nations became increasingly hostile and large populations immigrated to their ethnic states. After the Greco-Turkish war of 1919-21 a population transfer treaty was signed between Greece and Turkey, transferring all Greeks in Turkey to Greece and all Turks in Greece to Turkey (except Greeks in Istanbul and Turks in Western Thrace). Remaining Turks in Western Thrace have mostly immigrated back to Turkey over time, while Istanbul Greeks have fled after the 1955 pogrom. Hence the homogenity of both countries now.
I would like to add related question:
Why did Serbia stay Christian (Orthodox) with very small number of converts, while in Bosnia there was significant part of population that converted to Islam under Ottoman rule?
A similar question was asked here.
Is it true that the Iconoclasts largely ended up in Eastern Anatolia and that secret Iconcoclasts might have been more amenable to Islamication?