Nice sleight of hand, but the 1948 Dixiecrats were not resisting the Civil Rights Act of 1964. The Dixiecrats were resisting, in effect, the XIVth and XVth Amendments—heck, they were practically resisting the XIIIth Amendment. But if the federal government has no legitimate authority to prevent states' violations of Constitutional rights reserved for the people or prohibited to the states, the entire document becomes meaningless. If the federal government cannot enforce the XIVth and XVth Amendments, then it also cannot enforce Article IV, Section 4, and there's nothing to prevent a state from reverting to monarchy.
I absolutely concur that the civil "rights" movement of the 60s trampled the Constitution by equating private, voluntary action with coercive government action. However, the Democrats of the 40s had no more respect for freedom of association than the Democrats of today do. Strom Thurmond repudiated their beliefs long ago, and I'm stunned that so many Republicans here find it hard to do the same. Just because the Dixiecrats used to be the enemy of our enemy, that does not make them our friend.
Remember that as early as 1938, conservative Southern Democrats were expressing their dissatisfaction at Franklin Roosevelt by opposing his "court packing" schemes. Increasingly during the 1940s, the conservative Southerners were beginning to find common cause with Republicans.
The Dixiecrat movement was, like George Wallace's American Party 20 years later, a halfway house between the white South out of its century long alliance with the Democrats and into the GOP. That there is now a two party South is in part due to the migration of conservative Democrats away from the party of Jefferson and Jackson to that of Lincoln and Theodore Roosevelt.