I agree we are in the wrong forum, we need a POD during or before the Civil War to enable a more deeply grassroots Reconstruction after it. Getting Congress to be determined by a form of Proportional Representation, aggregated nationally, would help by automatically undercutting any venue that suppresses the vote. To enable that needs a different form of the Union political coalition during and after the CW and also a strong dependence on African-American self-liberation via regional organized comprehensive slave revolts (with Union aid) and post-war strong organization of black-majority regions. I do think they need to enact PR and make it the national norm and equivalent to the definition of democracy to cement the deal. All of that might put enough of a spoke in the Redeemer wheel to make white supremacism limited regionally, strongly challenged when most in ascendency, and eventually erode away its legitimacy in hard core supremacist regions.
Ain't nothing going to make it vanish overnight, but if people who aren't exactly comfortable with interracial political coalitions can nevertheless stick to them and profit by them, the next generation will have a wider pool of open-minded people and around them, a wider one of people willing to deal with the minority race for pragmatic purposes and shrug off accusations of race betrayal. And so on.
A lot of socialism would help, but it has to be socialism for all races. The US Socialist Party I am afraid tended to throw black people under the bus. I would like to hope the membership was less racist than the US norm at the time but that is a low bar to clear, and I believe the party did choose strategically to steer clear of racial "controversy" in an effort to maximize possible appeal to the Southern white majority. And that is fatal because the function of the perceived "black race" in post-slavery America is to be last hired, first fired, and other wise serve as the shock absorber of the cyclic bumpy ride the capitalist cycles inherently create for workers. By taking a lot of the sting out of it it was easier for the white majority to accept capitalism without the belief that their lives would suck until they got democratic control over it through a democratic socialist state that could override capitalist decisions. Without that belief, that "they had nothing to lose but their chains" essentially, allowing for some relativism, socialism had limited appeal that dissolved away completely except for fringes and diehards in post-WWII prosperity. And as long as the working class is mainly accepting of an untamed capitalist regime, someone or other in the working class must take the hits of the cyclic downturns. By making people of color take it the hardest, white workers got a smoother ride; if the working class and their bosses went colorblind, the average, voting worker would have a harder time of it during the downturns and thus be more liable to radical solutions. Playing it safe on race doomed the Socialists of the USA. Playing it fair between workers means white workers suffer equally along with black; accepting discriminatory policies cushioned the quality of life for white workers and thus made them actively complicit in the national apartheid system of double standards, and of course alienated the two races from one another.
So I'd aim for a trifecta of 1880s-'90s radicalism leading to a big tent social democratic victory that would not necessarily go so far as to abolish capitalism, but would at least claim the power, in the name of the working majority of the people, to tax and regulate it so as to smooth out the bumps for the working class as a whole. If we come out of the 19th century as laissez faire as OTL, then the temptation to throw people of color under the bus and rationalize it with essentialist racist nonsense of any kind, be it race-theory and pseudo biological or a culture based theory ignoring the systematic social machinery at work, and either would undermine the ability of a populist social democracy to set sensible policy.