What were the ideals of Southern Democrats before 1960? Segregation.
As in the years before the Civil War, you'll see a lot of talk about "states' rights," but that term is window dressing for the reality. Just as in 1860, southern politicians used "state rights" as a shadow puppet for slavery, so too was the idea of "states' rights" in 1960 a dog whistle for segregation.
As an Alaskan and someone who studies Alaska history, I come to this subject from a perspective you might not have thought of. Southern Democrats before 1960 were the key stumbling block against statehood for Alaska and Hawaii. Southern Democrats, particularly in the Senate, were strongly against statehood because they knew that the addition of four senators and however-many Representatives would worsen the odds of preserving segregation.
Terrence Cole's Fighting For the Forty-Ninth Star is a work devoted to this idea, and I think no single quotation sums this up better than a paragraph attributed to George Lehleitner, a New Orleans businessman who in the years immediately after World War II campaigned hard for Hawaii statehood.
Common wisdom at the time was that Hawaii, more economically developed, was a better candidate for statehood than Alaska. In his campaign, however, he found himself confronting opposition in the House and Senate. Southern Democrats held prominent committee positions and were in positions to block any statehood movement. A frustrated Lehleitner wrote in 1957:
"when one of these Southerners tells you that he is very much concerned about 'States' Rights' what he really means is that he is very much concerned about the issue of segregation," Lehleitner said. He mentioned this simply to guard against the possibility" that someone might "take those fellows seriously when they profess a deep concern about 'States' Rights.' I can only repeat that their REAL concern is primarily about the segregation implications."
You can see this physically in the 1948 presidential race. After Harry Truman established the President's Committee on Civil Rights and ended segregation in the U.S. military with an executive order, southern Democrats seceded from their party and nominated Strom Thurmond of South Carolina for president. Thurmond, running under the banner of the States' Rights Democrats (better known as the Dixiecrats), won Mississippi, Louisiana, Alabama, South Carolina, and an elector from Tennessee. The result nearly threw the election to Republican Thomas Dewey, one of the two men in the famous "Dewey Beats Truman" headline.
The big switch came in the 1964 Presidential Election. In that election, noted conservative Barry Goldwater became the Republican presidential nominee and a Democratic presidency (and Congress) approved the Civil Rights Act. Goldwater lost, but he carried his home state as well as Louisiana, Mississippi, Alabama, Georgia, and South Carolina. The famed drama of Goldwater's presidential run in hindsight looks like the turning point.
The Southern Strategy played a huge role in this shift, from a Berkley Article:
The so-called ‘solid South’ did not become solidly Republican overnight. Republican strategies began to stoke racial resentment and antipathy to civil rights. For example, Nixon campaign advisor Kevin Phillips and RNC Chairman Lee Atwater admitted appealing to white resentment to civil rights and even white racism. They did so not only by criticizing federal civil rights legislation and impugning federal desegregation orders, but by railing against busing, government dependency, and welfare, or by espousing such seemingly race-neutral ideas as “states rights” and “local control” as signals to preserve Jim Crow from federal intrusion. Even without making explicitly racist comments, the “dog whistle” was clearly heard by those who were its intended recipients. These strategies, combined called the “Southern Strategy”, was designed to create a national Republican majority, built, in part, on white resentment.
This still affects party demographics to this day.
I would add the cumulative effort of the 1960s counterculture, youth movements, campus protests, changing gender role, and the rise of black power movement. The South will always be a socially conservative, change averse society. In a time of upheaval Nixon jowly promises to resolve Vietnam with dignity and talks of a silent majority were also a factor.
Great question and great responses.