What a vague and arbitrary question. How do you define racism? By modern and especially Atlas standards 90% or more of white southerners (and whites in most areas of the US) would have been “racist” until the 80s or 90s. What do you define as the South? Only the former confederacy or do you include Oklahoma, Kentucky and West Virginia?
By modern standards and having a loose definition for the South Truman and LBJ most likely beat Thurmond and Goldwater in this “demographic” by virtue of winning more (and generally states with a larger voting population) Southern states. In regards to 28, 52, 56, 68 and 76 it was probably quite close and for 60 I’d give JFK an advantage.
Truman in particular probably got a plurality of such voters, given that in contrast to Johnson, he also carried Georgia, and did so by the typical landslide margin that Democrats obtained in the state at every election prior to 1964. In Georgia in particular, Truman beat Thurmond and Dewey 61-20-18, prevailing over their combined totals by a margin of 23%. And in 1964, Johnson won the votes of many deeply racist, pro-segregationist whites throughout the Upper South, particularly in states like Arkansas, Tennessee, and North Carolina, because of their objections to Goldwater's domestic and foreign policy proposals, particularly war (ironically enough), the TVA, and federal farming subsidies. In South Carolina, Louisiana, and Georgia, it's obvious that many racist whites still voted for Johnson, since he cleared 40% in those states. Even in Mississippi, Johnson got over a third of the vote in Northeastern counties that were part of the TVA's mandate and had some concerns about Goldwater's economic policy, though race won out for them more, as it did for the entire state.