The early Christians of Kapodokya were the victims of Roman persecution and Arab and early Seljuk raiders, but I think it's important to remember that people were carving those subterranean cities out of the tufa easily 1000 years before the Christians were.

I don't know the precise history, but I think, in the long run, the Kapodokyans just got assimilated into the ebb, flow, triumph and turmoil of Ottoman and, later, Turkish life. Kapodokya straddles such a huge area, and it saw waves of Persian, Macedonian, Greek, Roman, Armenian, Byzantine, Arab, Crusader, Seljuk and Osmanli armies, tradesmen and pilgrims continually crossing through it. I wonder what language those early Christians spoke ... some form of ancient Greek, maybe? ... but I'm sure they began to gradually adopt Turkish as the sultans consolidated their rule on central Anatolia ... and so often language shapes cultural identity. The two times I went to Turkey, I met many, many friendly and interesting people, and I was always amazed at how far-flung their family histories were; some were of Albanian or Macedonian or Greek or Bulgarian ancestry, while others were Kurdish or Armenian or Laz ... but they spoke Turkish and considered themselves Turks first and foremost.