Given how the CSA actually worked, I can see poor whites splitting and backing a 1900s communist revolution. Meanwhile the USA reacts by suppressing the labor movement more.A Communist CSA is interesting but less likely than a Communist USA. The reason for that is of course racism. Poor blacks and whites in the South were and are the majority and are in TL-191 but they never came close to uniting because of racism. The Radical Liberals never had very much white support in the CSA likely for the reason - it was felt they somehow supported black equality and rights with whites so a Communist CSA would have had the support of ever fewer whites and therefore not very likely ....
That might make a neat modem day story actually. The "Democratic People's Republic of America" is the last major communist state on Earth, an authoritarian regime described in patronizing terms by Western newspapers and channels, while the USA is a mostly democratic but corrupt capitalist superpower with a perpetually festive labor movement.