I've seen 'white' Roman Catholics from southern Italy that are far more swarthy than many Muslims from Iran or Lebanon. And I'd be hard pressed to visually distinguish an orthodox Greek from a muslim Turk... So yes, it's very much a socially constructed matter. Incidentally I believe Arabs, Persians, Turks, etc are often classified as caucasian (particularly on the US census I believe?) So these cultural definitions aren't even consistent within specific societal context. I've even seen some racists online say that Italians aren't white, because they aren't nordic.