Short Answer 
The 1960s marked a political realignment where many White conservatives moved from the Republican Party to the Dixiecrats to resist civil rights reforms. This led to the Republican Party adopting more conservative ideals while the Democratic Party embraced progressive principles, attracting more White liberals and Black individuals in support of civil rights and social justice.
Step 1: The Shift of White Conservatives
During the 1960s, a significant movement was observed where many White conservatives migrated from the Republican Party to the Dixiecrats. The Dixiecrats were staunchly opposed to the Civil Rights Movement and the integration efforts championed by liberal Republicans. This shift was driven by the conservatives’ desire to uphold segregationist policies and resist progressive reforms.
Step 2: Changes in Party Goals
This era witnessed a transformation in the fundamental goals and values of both the Republican and Democratic parties. The Republican Party began to adopt more conservative ideals, pushing away from its earlier moderate stance. Conversely, the Democratic Party embraced more liberal and progressive principles, which played a crucial role in reshaping voter alignment and loyalty across the country.
Step 3: Demographic Shifts within the Parties
The political landscape was dramatically influenced by the demographic transition, where a growing number of White liberals and Black individuals started aligning with the Democratic Party. This change occurred as the Democratic Party increasingly prioritized support for civil rights and social justice, appealing to these groups and fostering a significant shift in political allegiance that underscored the realignment of the decade.