Culture is the extension of ethnicity into the physical world.
Chinese culture is an extension of the Chinese and dictates what China is like, India is India because it is an extension of Indians.
If people were wholly interchangeable we'd have never gotten the disparity we see around the world in the first place.
But I can remember a time when Sicilians were barely considered "white."
And I'm not even all that old!
The term "white," at least in one sense, has a lot to do with belonging to the dominant culture. Where we have failed in the West over the past forty years is in insisting that immigrants join the dominant culture.
More and more people are finally realizing this, hence the discussion of the failure of multiculturalism.