I'm reading up on the Civil War and Reconstruction era South for an AAR over on the Paradox forums and I believe there is room for multi-racial radicalism. After all, race relations would probably be equally unequal de jure when slavery is eventually abolished in a free Confederacy but de facto I doubt it would quite so bitter, at least on the white side.
The southern wing of the Populist movement, the Farmer's Alliance, did have cross-race support and although it was segregated with 'Coloured' sections, its leaders often spoke of striving for class-based rather than race-based unity.
Most importantly I don't think Marx would hold much sway in the CSA - Proudhon however. Any radical left-wing movement in my mind would be syndicalist.
Using the rather clunky method of comparing real-world American radicalism, with societies like Russia and Spain, its obvious that Unions, Agrarian collectives and the cooperative movement are the obvious ways forward.
After all, if the comparison to Russia, the Bolsheviks only came to power through very specific circumstances, while in Spain, it was the Anarcho-Syndicalists that held the most support.
I can imagine in the early 20th century, a Farmer-Labour Party forming, based off the remnents of the Populist movement, and inbedded in the cooperative societies.
Also looking at how the Democrats dealt with Populism, by co-opting and race baiting, I imagine they themselves will become 'populist' and develop something of a Tory Democracy bent. Actually I can see them becoming similar to the Ulster Unionist Party, during its supremacy over the Northern Irish Parliament in the 1920s-1960s. They will be a 'massenpartei', with rather cliqueish control over certain areas, ultimately leading to certain people becoming marginalised, such as the Hill-Billies, Blacks, Trade Unionists, Cooperators, etc.
Its from this exclusion, I think you could see poor whites look to their black neighbours as allies. That said, I still imagine such a movement to be massively dominated by whites at the top, while seperate organisations focus on black issues.
Due to white control of the state and the economy, I imagine radicalised blacks will ultimately look to Anarchism, as natural extension of the mutualist experiments of the freed sharecroppers. Some will then ultimately go further, and become adherents of Propaganda of the Deed.
Ultimately I think you'd need a major upheaval such as *WWI to do it, but a revolutionary socialist state is just about possible IMO. Its just how long it will last with the USA sitting up top. I think the Federation in EdT's TL offers some ideas of how I imagine the People's Confederacy to look. Ultimately a state similar to the USSR in some respects but syndicalist in intent and little to do with Marx or Lenin.
It would be interesting to see how Africanism develops in the CSA, or how many blacks might emigrate up North, if they're allowed that is.