Anthropology

The underground cities of Cappadocia date from about 300 BCE and were likely built by Phrygians, not Christians or Jews.

Chances are they started out as shelters from volcanic eruption or climate catastrophe, not sustained military conquest or religious persecution. While they had pens for livestock and facilities for stored grain and livestock feed and deep cisterns for water, they were most likely occupied only episodically and for brief periods. People and livestock just don't do well underground, making it unlikely they were occupied sustainably over months or years.

It will be some time before they nail down how long ago the bolt holes were first begun and who had the bright idea of going to ground, but my best guess is that less elaborate accommodations long predated the Phrygians. There are multiple levels at Cappadocia and those had to have been the work of generations and most likely of different peoples for different reasons. However romantic the idea of "Roman catacombs east" might be, I find that the least likely explanation for those elaborate bolt holes.