Essentially when President Lyndon Johnson got up before a joint session of Congress and used the phrase "we shall overcome" which had become the anthem of the civil rights movement, that's when the Dixiecraft wing of the Democratic Party bolted in mass to the Republicans. What had been a trickle became a flood.
Most of these individuals were from the old Confederacy states that wanted to preserve "states rights", which simply meant the societal status quo. Let's just say civil rights was not at the top of their agenda.