Republicans are certainly not attacking Rice simply because she is a black woman. But it is certainly likely that they are attacking her because she is a black woman, allied with a black man, who represents the party which black America believes is the best vehicle for its particular interests, and the broader interests of the country. In other words the question isn’t “Is Senator Lindsey Graham racist?” so much as it’s “Who does Senator Lindsey Graham represent?”
The answer is Graham represents a party whose candidate for the presidency believes black Obama voters are guilty of the sin of electoral bribery, while white Romney voters are simply guilty of loving their country too hard. Graham represents the party of birther claims and birther jokes; the party which thinks attempting to restrict the votes of black and brown people is good use of their resources. The notion that you can separate who Republicans target, from how their base tends to evaluate those targets is willfully naive.
It does not matter what dwells in Lindsey Graham’s heart. No one knows. The hard interests are what matter.