The controversy inspired by Hillary Clinton’s remark crediting Lyndon Johnson with the civil rights movement’s successes seems to have subsided. Contrary to much recent punditry, this contretemps does not prove that the Democratic primary has been reduced to a zero-sum game of identity politics. Rather, it reveals the complexity of bringing together the aspirations of different social groups within a single political movement–something Americans have experienced before.

Some commentators have already compared Barack Obama to Frederick Douglass, the former slave and crusader for emancipation who insisted that the post-Civil War years constituted the “Negro’s hour” and that the struggle for the rights of the newly freed slaves took precedence over gaining the vote for women. In this scenario, Hillary Clinton is a latter-day Elizabeth Cady Stanton, who broke with her male allies when they called on women to subordinate their claims. But like many historical analogies, this one distorts as much as it reveals.

American feminism was born of the abolitionist movement, with its powerful insistence on universal equality. Before the Civil War, abolitionists and feminists, male and female, worked together for an end to slavery and a new definition of citizenship in which rights would not be limited by race or gender. During the war feminists put aside the campaign for women’s rights to join in the struggle to save the Union and free the slaves. But they saw Reconstruction as a golden opportunity to claim for women their own emancipation.

In the war’s aftermath, Congress rewrote the Constitution to guarantee equality before the law for blacks and the right to vote for black men. The Fourteenth Amendment, ratified in 1868, decreed that all people born in the United States were citizens who must enjoy equal protection of the law. But for the first time, the amendment introduced the word “male” into the Constitution, in a convoluted section related to voting. It punished states that failed to enfranchise black men with a loss of some of their seats in Congress. There was no penalty when women were denied suffrage. The Reconstruction Act and the Fifteenth Amendment barred states from denying the right to vote on the basis of race but left them free to do so because of gender.

These measures launched the era known as Radical Reconstruction, the first experiment in interracial democracy (for men) in our history. For the first time, large numbers of African-Americans voted and held office. Mississippi elected two black men to the Senate. (In the century and a half since, only three have followed, including Obama.)

But feminists like Stanton saw abolitionist support for these laws and amendments as a betrayal of the movement’s long-standing commitment to full equality. A bitter controversy ensued, which resulted in Stanton and her supporters cutting their ties with their allies and forming an independent national organization to promote women’s suffrage. They now felt free to appeal to racial and ethnic prejudices, arguing on occasion that native-born white women deserved the vote more than nonwhites and immigrants.

This episode has come down to us as the feminist-abolitionist split. But the story is more complicated. What actually happened was a split within the feminist movement. Nearly every black feminist supported the Fourteenth and Fifteenth amendments. So did many white women. Supporters believed these measures were necessary to protect all African-Americans from oppression in the aftermath of slavery. They saw the enfranchisement of black men as a step toward universal suffrage, not a retreat from it. Women like Abby Kelley, one of the era’s greatest feminists, formed their own women’s suffrage group, still linked to the abolitionist tradition. Not until the 1890s were the rival organizations reconciled.

The point is not that one position was right and one wrong–either in 1868 or 2008. During Reconstruction, both sides offered cogent arguments. One thing we can learn from their experience is that debating who is more oppressed is a fool’s game. Advocates of the rights of African-Americans and women achieve more working together than fighting among themselves.