Gets, as your post seems to indicate, you recognize that race and ethnicity are functions of DNA; place of birth or upbringing are irrelevant. Also, your reference to Sicily is a good illustration since it has experienced its share of invasions by the French and Muslims (just to cite a couple) and the Muslims could have originated in Egypt, Arabia, Persia, or what was generally described as Mesopotamia and subsumed any number of ethnicities.

Also, Jewish is not a race or ethnicity. Some who adhere culturally or religiously to Judaism can trace their ancestral origins to the Hebrews or Aramaics, but it's a long shot.