I've never heard the terms Caucasian Italians or white Italians.
Why do people emphasise that Italians are white? We know we're white people refer to them as "Caucasian Italians" no one say "Caucasian German" or "Caucasian French"
Never heard of it.
I refer to myself as American Human or Human American or if you want to be politically correct Human :)
I never heard of such thing either!!
What you've experienced is just one forum and unreliable to consider it a "Majority" or the state of "Everyone" doing that! Because such thing doesn't really exist! You be Caucasian you'll be consider as one regardless of any label of where you came from!
Since it's just this forum and youtube video that you've mentioned in the comments, probably those sources talking about none mixed faces of Italian.
I mean just like, right now Italy's football national team has two player "Mario Balotelli" African-Italian and "Stephen El Sharrawy" Egyptian-Italian.