During the last century, the assumption was that during the reign of the Lusignans the Latin elite oppressed and despised the Greek Orthodox majority. However, historians of the 21st century have uncovered a wealth of evidence that suggests rather than tensions or mere tolerance, the dominant feature of religious life in Frankish Cyprus was mutual respect and joint worship.
The Greek Orthodox Church was undoubtedly impoverished by the exodus of wealthy Greek aristocrats who had been it's most lavish patrons. It lost some of its economic land-holdings as well, but it retained all its churches and the tithes of the Orthodox population. The Latin Church, in contrast, had a very small population of Latins which it could tithe and otherwise had to live from donations. Notably, the secular lords of Cyprus repeatedly backed the Orthodox Church in stopping the Latin Church from claiming the lands of the Greeks -- in large part to protect their own properties!
Greek Orthodoxy survived the Frankish period not so much because of a successful national struggle against complete absorption as because the Greeks always remained the majority and neither the Franks nor the Latin Church ever attempted any Latinization. The Latin Church required what it thought was the bare minimum from the Greek clergy -- nothing from the Greek laymen -- and the Greek clergy gave the Latin Church what it required, including by the end of the thirteeth century, an oath of obedience from the bishops and an end to active opposition concerning unleavened bread. Almost all other particulars of the Greek rite, what we now call Greek Orthodoxy, were allowed to remain the same. [Chris Schabel, "Religion" in Cyprus: Society and Culture 1191 - 1374, editor Angel Nicolaou-Konnari and Chris Schabel, 201; italics addded by HPS]
In short, Cyprus was effectively without its legal rulers either secular or ecclesiastical for this critical period. It appears that this fact was exploited by outsiders with no history of peaceful co-existence. At the urgings of a certain Dominican friar -- the Order of the Inquisition and possibly fresh from fighting the Alibigensians -- the Greek Orthodox monks were condemned to die a heretic's death. Yet, as the documents prove, they were not condemned because they used leavened bread, but rather "because for years they refused to stop calling the Latins heretics for using unleavened bread." Schabel suggests that despite knowing that the pope did not consider the use of leavened bread heretical, the Dominicans could "not tolerate the Greek accusation that they were heretics for their practice." (Schabel, 196).
For more on the disputes between the Cypriot clergy and the pope as well as the evolution of unique art forms see: Nicolaou-Konnari, Angel and Chris Schabel (eds). Cyprus: Society and Culture 1191 - 1374 (London: Brill, 2005).
My most recent novels set in medieval Cyprus reflect this overall atmosphere of inter-faith cooperation punctuated by moments of tensions: