The mass immigration that followed the Irish famine of the 1840s inflamed nativist, anti-Catholic bigotry that flourished through the end of the century. Then new waves of poor Eastern and Southern European immigrants arrived, inspiring new racial classifications: the “Northern Italian” race, the “Southern Italian” race, the “Eastern European Hebrew” race, and so on. Their heads were measured and I.Q.s assessed to quantify (and, later, to deny) racial difference. They were all white, members of white races. But, like the Irish before them, the Italians and Jews and Greeks were classified as inferior white races.

By the early 20th century, the descendants of the earlier Irish immigrants had successfully elevated Celts into the superior realm of northern Europeans.

Meanwhile, World War I dampened Americans’ ardor for “Saxon” — given its German associations — and increased the popularity of a new term liberated from Germanic associations. The new name was “Nordic.” Many German-Americans even altered their surnames during and after the war, but the notion of plural white races held on until World War II.

By the 1940s anthropologists announced that they had a new classification: white, Asian and black were the only real races. Each was unitary — no sub-races existed within each group. There was one Negroid race, one Mongoloid race, one Caucasoid race. Everyone considered white was the same as everyone else considered white. No Saxons. No Celts. No Southern Italians. No Eastern European Hebrews. This classification — however tattered — lives on, with mild alterations, even today.

The useful part of white identity’s vagueness is that whites don’t have to shoulder the burden of race in America, which, at the least, is utterly exhausting. A neutral racial identity is blandly uninteresting. In the 1970s, long after they had been accepted as “white,” Italians, Irish, Greeks, Jews and others proclaimed themselves “ethnic” Americans in order to forge a positive identity, at a time of “black is beautiful.” But this ethnic self-discovery did not alter the fact that whiteness continued to be defined, as before, primarily by what it isn’t: blackness.

Ms. Dolezal seems to have believed that the choice to devote one’s life to fighting racism meant choosing black or white, Negroid or Caucasoid. Black was clearly more captivating than a whiteness characterized by hate.

We lack more meaningful senses of white identity, even though some whites, throughout history, have been committed to fighting racism and advocating for social justice. In the 19th century, abolitionists like William Lloyd Garrison and John Brown helped end slavery. In the early 20th century, Mary White Ovington helped found the N.A.A.C.P. Lillian Smith depicted the South’s nexus of “sin, sex, segregation” in her writings. White Communists, priests and rabbis stood beside the Rev. Dr. Martin Luther King Jr. during the civil rights movement. Where would America be without these white allies of black freedom fighters?