This Southern Strategy of Nixon is still largely a myth. Some of the Democrats believe so strongly in it because it makes you feel better about your party. It makes you feel better that the party of slavery, Jim Crow and the Klan has somehow cleansed itself. Nixon didn't convert your racists to Republicans. Just look at prominent Dixiecrats. Except for Strom Thurmond most of them stayed Democrats. Robert Byrd never left the party. Neither did George Wallace or Al Gore Sr. When Nixon won in 1968, supposedly employing the "Southern Strategy," Democrat George Wallace won the deep south states. This alone should give the "Southern Strategy" believers pause. It doesn't support your theory at all. Nixon basically didn't even campaign in the south in '68. He concentrated on the north and the Sunbelt. Nothing Nixon ran on was racist. "Law and order" isn't racist. A majority of Americans didn't have positive opinions of "hippies" protesting the Vietnam war. "Law and order" appealed to them. Nixon supported Civil Rights and he supported Affirmative Action. He was ultimately a crook, but he never ran on racist policies. Besides he won in landslides in the North and the Sunbelt in 1968 and won nearly every state in 1972. Again, it doesn't support the theory. Atwater is a single person. He's not the party. What Atwater said in no way proves that he had a say in what the party did or that any prominent Republicans really bought into what he said in an interview years after the supposed implementation of this "strategy."
More southern Democrats became Republicans as their economic situation improved. That plus social issues (abortion especially) were the keys for Republicans gaining popularity in the south. Of course some racists have probably come to favor the Republican party because they THINK they're more comfortable there, but make no mistake, there are plenty of racists in the Democratic party too.
I'll depart with the comment I overheard in 1980 from a prominent Democratic activist in Bloomington when I was helping with the Carter campaign (to be honest, helping very little, as I was more preoccupied with partying, but I passed out a few flyers and attended a meeting or two
). I was shocked when I heard the guy tell another guy, "I'd vote for the blackest N-word before I'd vote for a Republican." Obviously that solid Democrat (and racist) hated Republicans more than he hated black people. Racists live among us, obviously.