It's remarkable how quickly and easily people who otherwise appreciate nuance and complexity become reductionist vis a vis race.
Firstly, systemic racism exists. If there were two babies born in America with equal innate intellect, capability and temperament -but one was white and one was black... and the white kid grew up in a median "white" home, and the black kid grew up in a median "black" home, the white kid would be more likely to get a good public school education, more likely to get into college, would make more money, and would be less likely to end up in prison. Is this because there are evil racists keeping the black kid away from opportunity?... probably not. However, the median accumulated wealth of a white family is ten times that of a black family. This translates into better neighborhoods, lower crime, better schools. In these better neighborhoods, people walking down the street are less likely to be arrested... and when they are, they are less likely to end up in prison. The wealth difference is multi-factorial, but it would be foolish to disregard the very recent practice of "redlining" which prevented many AAs of all income brackets from getting loans to purchase houses in nice neighborhoods until VERY recently (homeownership being the primary vehicle for wealth accumulation in America). While this is no longer the case today, AAs are less likely to have wealth passed down from the parents because of these recent practices. This is to say nothing of laws like the crime bill which sent people away for possessing 5 g of crack (a drug more prominent in AA communities) for decades while 10x as much coke (a drug more prominent among whites) was punished with a lower sentence -again, this is no longer the case, but the damage was done. There are countless other examples of laws, rules, and practices that have been (and still are) disproportionately punitive to AAs and other minorities.
On the other hand, there are MILLIONS of white Americans for whom the word "privileged" would seem a gross misrepresentation, and there are plenty of AAs who grew up in affluent homes with ample opportunity.
My personal take is as follows. Systemic racism exists, but the term "white privilege" misses the mark. Privilege is defined: a special right, advantage, or immunity granted or available only to a particular person or group. If we acknowledge that white people, collectively, have more opportunities than black people do (and we should)... we should ask ourselves, are these opportunities "special"? Not growing up in poverty and not going to prison for decades on a small-volume drug charge doesn't strike me as "special"... it strikes me as the way things should be for everyone. Also, we think of a "privilege" as something that one can lose... should white people lose their safety and opportunity to foster equality? No.... that wouldn't solve anyone's problems. Lastly, there are many white people who have had hard lives and they don't need to bear the shame of being called "privileged" while they struggle to feed their families. It's like you get a 68% on a test and someone grabs your test, throws it on the ground, and screams "it's not fair, you got the easy version". I just don't see the term "white privilege" convincing anyone of anything... and is likely an obstacle to addressing systemic racism.