The idea that the Civil Rights Act turned the South against the Democratic Party doesn't make sense when the South continued to vote for the Democratic Party for another 40 years including in Presidential Elections. An electorate blasting McGovern and Mondale is nowhere near as good of supporting evidence as looking at every level of the state including U.S. Senator, Representatives, Governor and the state legislatures.
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Presidential Popular Vote Share between the two parties in the 11 Confederate States:
2012 - 54.3% R, 45.7% D
2008 - 53.1% R, 46.9% D
2004 - 57.2% R, 42.8% D
2000 - 55.5% R, 44.5% D
1996 - 50.0% D, 50.0% R - Dem Candidate incumbent from Arkansas
1992 - 50.8% R, 49.2% D
1988 - 58.7% R, 41.3% D
1984 - 62.6% R, 37.4% D
1980 - 53.6% R, 46.4% D
1976 - 54.8% D, 45.2% R - Dem Candidate an evangelical from Georgia
1972 - 70.6% R, 29.4% D
1968 - 52.8% R, 47.2% D
1964 - 51.3% D*, 48.7% R - Civil Rights Act passed
1960 - 53.6% D**, 46.4% R
1956 - 50.6% R, 49.4% D
1952 - 51.8% D, 48.2% R
1948 - 65.5% D***, 34.5% R
1944 - 74.0% D****, 26.0% R
1928 - 52.4% D, 47.6% R
1920 - 63.4% D, 36.6% R (National: 63.9% R, 36.1% D)
1916 - 74.0% D, 26.0% R (National: 51.6% D, 48.4% R)
*50.4% D, 49.6% R if discount Unpledged Democratic Alabama votes
**52.3% D, 47.7% R if discount Unpledged Democratic votes in LA and MS
***73.3% D, 26.7% R if give all Thurmond votes to Truman
****74.8% D, 25.2% R if Upledged given to Roosevelt