Lee Atwater has this to say about Republican politics of 1980s:
"All that you need to do to keep the South is for Reagan to run in place on the issues that he's campaigned on since 1964, and that's fiscal conservatism, balancing the budget, cut taxes, you know, the whole cluster. ... You start out in 1954 by saying, "Nigger, nigger, nigger". By 1968, you can't say "nigger" — that hurts you. Backfires. So you say stuff like forced busing, states' rights and all that stuff. You're getting so abstract now, you're talking about cutting taxes, and all these things you're talking about are totally economic things and a byproduct of them is, blacks get hurt worse than whites. And subconsciously maybe that is part of it. I'm not saying that. But I'm saying that if it is getting that abstract, and that coded, that we are doing away with the racial problem one way or the other. You follow me — because obviously sitting around saying, "We want to cut this", is much more abstract than even the busing thing, and a hell of a lot more abstract than "Nigger, nigger". So, any way you look at it, race is coming on the back-burner."
I would say that the present state of the Republican party is very much in line with that, except that race didn't ever truly come onto the back-burner; somehow they're still talking about "those people" all the time.
So, Republicans are the party of white people who are proud that they are white (and annoyed that they can't show their pride openly anymore), while Democrats are the party of white people who feel guilty about it (and annoy everyone else by trying to make everyone aware of how badly they feel about it).