Italians are all mixed up?

I am a 3rd generation Italian who grandparents from both sides came from Sicily and the Roman region. I am light skinned,tall,red brown hair, and slanted hazel eyes. In school I would get teased about being Asian. Since living on the east coast, there are many Southern Italians who came at the the turn of the century. I know the Middle east had invaded Italy, along with many others, so then how can we say we are pure Italian?