...fact is that the overwhelming majority on the island is not "Turkish". What was "Turkish", by the Treaty of Lausanne, became "British". Cyprus now, is "Cypriot".
Although, you may feel it is unfortunate that the dwellers of this island speak mostly Greek, it has been the case for thousands of years. In any case, to survive, in the Modern world, and to thrive beyond, Cypriots know better than to count on their "Greekness", or their "Turkishness", to secure success in the efforts they make toward social-exchange, particularly with the rest of the world. Cypriots need more than the Liberty of representing themselves as distinct identities, they need for their Freedom, an identity as Individuals, where they can demonstrate their unity as such, toward Universal Principals.
"You" must trust the others, "they" must respect you: such is the way of the world. While there exists a Greek Flag, and a Turkish Flag, so too, there exists a Cypriot Flag; above all else, let's remember, we are Human beings by acting accordingly.