Actually they did and have, that's not to say by 1960 there wasn't a significant minority still in opposition.The majority of Southern whites never accepted racial equality. It wasn't that the timing was right or wrong the lesson of Reconstruction is that terrorism is very effective unless there is an counterinsurgency policy. When the Klan was opposed by effective state militas the retreated. When the federal forces withdrew then racist Democratic Party goverment's implemented racial discrimination.
If someone try's to overplay a poor hand they can't support, the blame rests with those who overplayed the bad hand with no support. Its called being realistic....
The Democratic party didn't impliment anything, they represented the status quo, which is what the majority wanted, hence they won.
If Republicians had indeed wanted civil rights, and to be successful, they needed a Freedman's Bureau pushing northern immigration......but they didn't, we can guess why. But as long as 90% of blacks lived in 12 states that were over 60% white and predominantly Democrat........you would indeed need to cater to those 60%.
Northern Republicians overplayed their hands with reconstruction as much as Southern Democrats overplayed their hands with secession.