I'd say it goes back to the very founding of the Republic and the refusal to face the slavery issue and to even consider the Native Americans as citizens or persons of equal worth.

That said, the issue with the Republicans in particular begins with the Cold War.  Before then, the party was primarily isolationist, and pro small government.  The Cold War jump started the worst elements of their party which had been out of power for 20 years until Eisenhower's election.  Eisenhower was a moderate, but he also acquiesced in much of the rhethoric directed at Democrats, including his refusal to disown McCarthy's remarks about George Marshall, his mentor and superior in WW2.