The Democratic Party's association with the civil rights movement is what has made it into the party that it is today. It is, in large part, why the Democratic Party is the party of non-whites today and the Republicans always win the white (especially the white male) vote.
After the civil rights movement, the Republican Party adopted their "Southern Strategy." In this strategy, the GOP appealed to whites who were turned off by the gains of the black movement and by the lawlessness of the Vietnam Era.
As the GOP took these voters away from the Democratic Party, the Democrats had to become more liberal and more pro-minority. The GOP turned the opposite way.
So the Democrats won the liberal and non-white vote, but they have pretty much lost the conservative and populist white vote for all of my lifetime up to this point.