FWIW, the GOP would probably do better among black voters, but bread-and-butter economic issues would still keep black voters a mostly Democratic voting bloc. Obviously an America where the GOP gets 25% of the black vote instead of 10% might be very different, but it isn't an America where the GOP is outright winning, unless there's some way the GOP ends up on the economic left of the Democratic Party.
IIRC, when liberal pro-civil rights Winthrop Rockefeller ran against Orval Faubus (also known as the Governor who stood in the doorway trying to block the Little Rock Nine), he lost black voters to Faubus by around 20-80.
Rural Southern blacks are not going to vote 90-10 Republican if Republicans are the more economically libertarian party. The rejoinder is "why have Republicans done so well with Southern whites since the 80's???" and my rejoinder is that outside of Appalachia, Southern whites aren't actually that poor anymore. Not particularly rich either, but mostly middle-class.
In Appalachia, where there are many more poor whites, Democrats easily won white voters until the 1990's and in some places, up until 2016. In poor, mostly white Elliot County, Kentucky, Barack Obama won 61% of the vote, compared to Hillary Clinton at 26%.
There's a tendency in alternate history to think that modern political divides and coalitions and what not are just random outcomes of "pivotal points" in history that we can have fun by changing in AH, but there's a powerful underlying logic to our modern political divides and something like a different President isn't going to really change that unless there are massive changes to the economy, society, culture, and the way people live. Certainly they can accelerate or slow changes, but they're often the consequences, not the causes of social changes.
For example, what we broadly call "neoliberalism" would have happened even if Reagan lost in 1980 - because you saw the same stuff happening everywhere in the industrialized world, even under left-wing governments.