So this is really interesting because it could have been decisive to elect Tilden in 1876. Which counterintuitively could keep the civil rights cause alive in the South into the long run because Republicans don't have any reason to capitulate.
I think we're not considering the butterfly effect or any cause-or-effect thing. Like we're asking independently which candidate it'd support in each race. Not like 'DC goes blue in 1876 and swings the race to Tilden,' because then 1880 is different, 1884 is even more different, and then we end up with a different TL which could be very different and feature different candidates. Too complicated.
But re: Tilden wins in 1876. Pretty sure Reconstruction would die anyway with a Democrat in the White House. Tilden was quite anti-Reconstruction, and Reconstruction was already on the decline. 1876 was just the final nail in the coffin: if Hayes won, it'd be because of
a compromise that involved giving in to the South on Reconstruction and ending it, and if Tilden won, which is the alternative, Reconstruction's dead anyway. But it makes me then wonder why Democrats would ever agree to giving Hayes the White House in exchange for ending Reconstruction when they could end it anyway - and enact the rest of their agenda - if they had their man in the White House. I guess it was basically because they knew Hayes was going to be treated as the winner anyway, and they were basically just threatening a lot of violence and rioting and refusal to acknowledge him as the winner (sound familiar?) if he didn't acquiesce to their demand and end Reconstruction.