There were areas of the South the GOP was competitive throughout the period. Eastern Tennessee was extremely doggedly Republican through the period, to the point that the GOP could occasionally carry Tennessee in Presidential years that the Democratic Party was divided or running a weak candidate.

Jim Crow didn't disenfranchise all African-Americans overnight...different states went at different speeds, and while the general trend of taking voting rights away from African-Americans took from 1875-1900, it was finished sooner in some states than others. Where more blacks could still vote the GOP did better.

The one great challenge to Democratic hegemony came in the 1890s from the Populist (or People's) Party, which had a strategy of seeing that while the North was competitive between the two parties, the South was overwhelmingly Democratic and the West overwhelmingly Republican and that they could become the second party in those regions. While out West the Populists sought votes from farmers and miners, in the South they pursued a strategy of gaining votes from poor sharecroppers, white and black alike, running a rabble-rousing campaign against the big cotton bosses. The Democratic powers that be feared this strategy and hastened Jim Crow to eliminate African-American political power and stirred up racial tensions and mob violence to prevent poor white and black coordination. Democratic politicians also adopted populist rhetoric (often without the substance) to further deny political room to the Populist Party.