But in the 60's, when blacks left the GOP and joined the Democrats, white conservatives fled the Democratic Party and filled the ranks of the racist GOP. And that's why the GOP is 90% white today.
That's part of it, but the shift of the black vote from Republicans to Democrats manifested in 1936, FDR's second campaign, and they've been there ever since. It did spike even more in 1964 though.
It's important to remember the sort of magnetic reversal of the political poles around the turn of the century (19th/20th). In Lincoln's day the young Republican Party was the home of Abolitionists, therefore Liberals, and also interestingly the home of doing Big Things with Government, a legacy of their other parent, the defunct Whig party (Lincoln had been a Whig). Meanwhile the DP was the home of "states rights" and opposition to Federal power, leaving powers to the several states.
By the end of the century the RP had abandoned its Liberal roots in favor of the interests of corporations and Big Business (see McKinley) while the DP had absorbed the Populist movement (see W.J. Bryan), which by definition served the interests of minorities, women, immigrants and blacks --- which coincidentally were all enemies of the second iteration of the KKK.
The South was the last entity to react to this polar shift, the idea of affiliating with the Party of Lincoln in any way, the man who had defeated and humiliated it in the War, being unthinkable for exactly 99 years after that war, with the result that Democrats in the South had less and less in common with Democrats anywhere else, because the South was effectively a one-party state until Strom Thurmond bolted in 1964, thereby making the unthinkable thinkable.
In 1909 when the NAACP was founded this polar shift was still in transition, so it's no surprise that its founders affiliated with the RP.