I don't know where the quote is from and pardon the language but this is a phrase I heard which touches upon this issue:
"What do you call someone who is 1/8th black in Montana? A white guy with a tan.
What do you call him in Alabama? A damn ______"
On a somewhat related note, sometime in the early 20th century a city in Virginia somewhere (can't remember which one) was going to pass an anti-miscegenation law defining anyone with non-European blood as non-white, until someone pointed out a large number of the city elite, including some of those considering the bill, were well known in local lore to be descendants of Pocahontas. The bill was quickly changed to define anyone with any African blood as black, but any white person with less than 1/16th Indian blood as white.
This is especially a pickle when you consider that there were groups we see as 'white' today, branded as 'black/colored' in the past, like Italians or Greeks, and god forbid you were Irish.
Living in the South, my brother went on this tirade that maybe Southern racism culture was overblown, and it certainly wouldn't effect him - until I pointed out that he, since he was dating a girl of Italian ancestry and he himself having been sired by an immigrant, Norse immigrant not withstanding, would be viewed by the Dixiecrat/KKK crowd as a race traitor. Changed his turn real fast.
Reason I bring that up is that getting folks to even agree on what 'white' is would be the place to start.