No state re-integrated into the Union on the basis of Reconstruction needs to own any pre-war history. There is no political continuity - the link is broken.
To see states like Tennessee prepare apologies for slavery is to see a modern polity voluntarily associate itself with an historical curiosity - as if Sarkozy were to apologize for the actions of Petain.
Further, it puts the government in the position of making a claim against the lives of Tennessee residents, the majority of whom are transients or descendants of non-Tennessee ancestors. It takes the fallacious idea of universal blood guilt and twists the principle around to produce an even more absurd "geographic guilt".
If some legislators seek to own the actions of a discredited and violently deposed slave government, surely there must be some punishment we can mete out to them without embroiling the entire population in political fantasy.
Meanwhile, as the apology law moves through state deliberations, the Republicans are opposing it on the basis that it might cost money down the road. Incredible.