Lordo, even i am against what you describe as a BBF (or "bbf"). Cyprus is one country, one State, whether within it Cypriots identify themselves' more distinctly, or not.
...it is a matter of what is natural. We are Cypriots, the stewards of this island, if we are to have self-representation then it is to be as Cypriots. In affect this is the great compromise, where the vast and overwhelming majority agree, as Greeks, that Cypriot, in defending each other, has a wider meaning that they are a part of.
The "Turks", like the "Greeks", have failed with their Agendas, there may be in Cyprus, some (not all), of "them". Now, Cyprus exists.