Although there's certainly much more to be said, you might be interested in this older answer where I expanded upon some aspects of societal evolution Southern Italy.

You might be most interested in this part of the answer:

Norman Sicily has been defined as a society based on "Unequal Coexistence." Although privileged positions were given to Norman, Provencal, Lombard, and Greek immigrants (more or less in that order) tensions between Christians and Muslims would only come to the breaking point in the late twelfth century. Tensions between Sicilian Greeks and the new "Latins" on the other hand, were easily overcome by professing adherence to the Church of Rome, only recently (in 1054) irreparably separated from the Church of the East, in Constantinople. Indeed, Greek Christians (who had in great part welcomed the Normans) played a key role in mediating between the upper class of Latin lords and the subject populations of Muslim serfs (according to Johns J., The Monreale Survey: Indigenes and invaders in medieval west Sicily). It's interesting to note how within a generation of the Norman conquest, parish censuses show how serfs whose parents have Arabic names take Greek names; a testament to the dominant "Greek Christian" culture in spite of the new Norman ruling class and the almost entirely Arab administrative bureaucracy, and more importantly, the key role of Greek Churchmen in converting the Muslim population to Christianity.

John Julius Norwich, in his The Normans in Sicily puts it this way: “Norman and Lombard, Greek and Saracen, Italian and Jew – Sicily had proved that for as long as they enjoyed an enlightened and impartial government, they could happily coexist; they could not coalesce.” Greek Orthodox inhabitants of Sicily could be expected to be fluent in Arabic, and some Muslims could be expected to be native Greek speakers. However, as with Arabic, Greek language and culture was also rapidly replaced in favor of Latin language and culture in Sicily and indeed all of Southern Italy. If you'd like to learn more, John Julius Norwich wrote a very extensive history of Sicily in two works, one chronicling the Norman Conquest and another on the actual history of the kingdom. Both works have recently been published together as a single work.