Central Anatolia was never densely populated anyway at any point, although it was probably enjoying growth alongside the rest of the Empire in the eleventh century. This came to an end after Manzikert, due to slow Turkish conquest (it's a mistake to assume that Anatolia fell rapidly after Manzikert, the process took over a decade) and then warfare caused by attempted Byzantine reconquest, as well as red hot Turk on Turk action.
I've read somewhere that Aleksios Komnenos' government supervised a partial evacuation of central Anatolia in the 1090s, but this should be taken with a pinch of salt: what'll be meant here is "a partial evacuation of those wealthy enough to up and leave". The vast majority of the surviving peasants will have remained long after 1100.
That being so, to answer the OP I'd guess the population at the end of the twelfth century probably tilted slightly further towards a Christian majority, but it would only have been a small one. Further Mongol-induced warfare in the thirteenth century would've further damaged the Christian populations of the plateau, so by 1300 there'd probably have been a comfortable Muslim majority. Thereafter, the trajectory was only downwards for the Christians of what was rapidly becoming Turkey.
As for elsewhere, the coasts retained comfortable Christian majorities for centuries longer: largely Orthodox, although there were pockets of Armenians across the region. I'd guess Muslims probably didn't become a majority in these areas until the eighteenth century or so, and of course the absence of a Christian population now is due to deliberate and forcible ethnic cleansing in the 1920s rather than any natural demographic decline.