False.
That those are Southern things is a hint that they are Southern things, and not only did Southern Republicans tend to go along, they formed a movement to do so, the Lily-Whites Republicans.
Meanwhile, not only did Northern Democrats not go along (seeing a pattern here?), a faction split off them to do so (Dixiecrats) when the party as a whole starting favoring and taking positions supporting civil rights, most famously starting with the 1948 DNC Convention,