Well, 1964 seems to be when the Republican Party began to play the "states rights" card, and otherwise appeal to reactionaries of every assortment. This seems to be largely in reaction to the Civil Rights Act.
However, it would be wrong to say that racism/ethnocentrism/xenophobia did not play a significant part in both parties, both before and after that. The parties were run by white people, and reflected to some degree or another the prejudices of the white constituencies whose votes they sought.
Not entirely sure I should have stated this in the past tense, because a lot of that is ongoing. It is just much more visible in the Republican Party today, because those who vote for that party are not sharp enough to hear dog whistles.