Religion is Religion and for the most part, outside of values, should stand aside.
Recreating any “Glories of Byzantium” has long been gone as far as the Greeks are concerned. They and others in the neighborhood would rather see a stable Turkey and such demostrations against fanatic Islamic groups then for them. Don’t forget Greeks and other Christians in Eastern Europe have the most to worry if Turkey takes a turn for the ala Saudia Arabia/Iran type of government; they would rather have living next door to them a secular Turkey then one made up of fanatic Grey Wolves types who burn effigies of every Patriarch Bartholomew out there every other day outside their homes.