Bull.
The KKK was a conservative organization. The Democrats cut their ties with them. Hugo Black and Robert Byrd actually apologized for having been members. In contrast, Trent Lott, Senate Republican Leader, never apologized for giving a speech to the Council of Conservative Citizens -- CCC, or, as they're also known, the KKK in suits and ties.
When Martin Luther King was jailed in Georgia on a BS charge in 1960, Coretta called the Nixon campaign, and begged them to get him out, because she was afraid he'd be killed in jail. Whether the plea ever got through to Nixon himself, I don't know; but the Nixon campaign did nothing. So Coretta called the Kennedy campaign. Somebody there got a message to Jack, who said, "Call Bobby." Bobby made a few calls, found a friendly judge, and Dr. King was sprung. And when that happened, Dr. Martin Luther King Sr. said, "If I had a million votes, I would give them to Jack Kennedy." I don't know if the black vote going to JFK made a difference, but that election was so close, it could have. If Nixon's people had gotten their man the message, and he'd done something about it, it would have shown that the GOP was still the party of civil rights, and it would have had consequences far more favorable to them in the long-term than Nixon beating Kennedy in 1960 would have been. The King family has been Democratic ever since.
Even Jackie Robinson, who worked for Nelson Rockefeller after he left baseball, and was a Republican as much for their "self-help" talk as for their ever-shrinking connection to Abraham Lincoln, saw the disgusting display at the 1964 Republican Convention and said, "It would make everything I worked for meaningless if baseball were integrated and America's political parties were segregated." Robinson voted for Lyndon Johnson in 1964 and Hubert Humphrey in 1968.
Wilt Chamberlain was also a Republican, pointing out that, once Nixon finally won in 1968, he did do things to help the poor, white and black alike. But he also said that, while he liked Nixon, he didn't like Reagan or Bush Sr., because their approaches to black Americans made Nixon look positively enlightened by comparison. (Yes, I read Wilt's entire book, not just THAT chapter. He was a fascinating guy, above and beyond his basketball skill.)
The Democrats' civil rights errors are in the distant past. The Republicans' are half a century old and ongoing.