As usual, Ben Shapiro is purposely getting some things wrong here. It's not that all of the "racist" politicians went from the DNC to the GOP. It's that the GOP started using the Southern Strategy to win over voters who were pro-segregation during the sixties, mainly starting with the Barry Goldwater campaign. They did this in conjunction with promoting "small government" as a justification for making segregation a state issue, as well as a way to appeal to rich businessmen who didn't want government regulation. Since then, the GOP has become the party of "small government" and conservative "values." The DNC accepted desegregation when they saw that this is where the country was going.
Today the DNC is very racially diverse, the GOP is virtually all white, and literally any group that believes in segregation votes Republican.
https://en.wikipedia.org/wiki/Southern_strategy