The melting pot is exactly where the ignorance comes from. It's easier to overlook the differences between an Irish and an Anglo when there's an African there too. Irish, Italians, and Jews probably gained their acceptance by using other races (e.g. blacks) as a common enemy (though that's just a guess, never really looked into it). Basically that LotR meme, but instead of dwarves and elves as friends, it's Anglo-Saxons and Italians as whites.
It's all the average American today has known. Discrimination more specific than continent of origin is seen as weird. Discrimination against different subgroups of the same ethnicity (e.g. burakumin in Japanese society) is seen as utterly absurd.