If White Privilege actually existed, we'd expect to see the following:
Affirmative action in favor of non-elite white people. In essence, any group that does better than white people in X would be expected to occupy no more than their own population percentage in X. So you'd see pre-1930's 'Gentleman's agreements' limiting the number of Jews and East Asians in elite positions or institutions.
Governments promoting affordable family formation for non-elite white people. Net transfer of fertility FROM other groups TO non-elite white people.
Immigration rules designed to benefit white people. Quotas for white countries much larger than those for non-white countries. Quotas massively reduced by multiples of the number of illegals from said country.
Massive law enforcement resources directed against X on white crime compared to vice-versa. Zimmerman case would be a non-event, black flash mobs would be ruthlessly suppressed.
Media would very rarely make negative or low status depictions of white people, especially white males. Other groups would be depicted more negatively than their actual fraction of negative behavior in reality.
So for those who profess to believe in White Privilege, does the US look ANYTHING like this?
For those who say this is 'over the top', most nations historically have done exactly this---just replace 'non-elite white people' with the group with demographic hegemony (e.g. Malays in Malaysia, Pacific Islanders in their own islands, etc). 'Affirmative action' to benefit the hegemon is really more the rule than the exception. Considering that neutrality seems to be impossible in practice, perhaps such 'White Privilege' is something to be in favor of, if one must be either hammer or anvil.