I am married to a Turkish Cypriot. She was born pre-1974 at the British Military Hospital in Nicosia, which did in fact create some difficulties later in life when she decided to apply for a 'kimlik' (ID card) in the TRNC. This was because neither administration would accept a British birth certificate as legal evidence of jurisdiction. Searches for a civilian birth record were conducted on both sides of the green line, and it took several years before one was found - in her case in the southern part of the island. Consequently, the ROC authorities granted her an ROC civil register number, which she was then able to use on the TRNC side to get her kimlik. I also believe that a ROC civil registry number will permit her automatically to obtain a ROC passport.
Her own sister on the other hand, was able to get her kimlik based on a birth record on the Turkish side. With her kimlik she was able to apply for and receive both a ROC passport AND a Turkish (mainland) passport.
The entire process although lengthy and time-consuming, evidenced goodwill on the part of authorities on both sides of the island. And even prior to starting this process, my wife was encouraged by the ROC consul in the country where we live, to apply for ROC citizenship.
From personal knowledge a very large number of Turkish Cypriots carry ROC passports, work in the south, have ROC social security numbers which permit them access health and other benefits. And of course gives them free visa-free access to the EU and many parts of the world.