Here's some nice, solid evidence of how much the Republican Party has changed since the 1950s. I'm going to present links to maps of electoral college votes from 1916 on.
File:ElectoralCollege1916.svg - Wikipedia, the free encyclopedia
This is a little misleading because it was a Wilson landslide, but note that Wilson (Democratic candidate in case anyone's forgotten) won the entire South, but lost most of the upper Midwest and Northeast states, as well as one state on the West Coast (Oregon).
File:ElectoralCollege1920.svg - Wikipedia, the free encyclopedia
In 1920, the Democratic candidate won almost the entire South (except for Tennessee) and lost everywhere else. The South voted Democratic, and the Northeast, upper Midwest, and West Coast voted Republican.
File:ElectoralCollege1924.svg - Wikipedia, the free encyclopedia
1924 was another big GOP win, but note once more: the Democratic candidate took the whole South. Republicans were weak there, and strong in the Northeast, upper Midwest and West Coast -- exactly the opposite of what we see today.
File:ElectoralCollege1928.svg - Wikipedia, the free encyclopedia
1928 was a Hoover landslide, so the outcome wasn't as pure, but again note that such strength as the Democratic candidate had was in the South.
File:ElectoralCollege1932.svg - Wikipedia, the free encyclopedia
1932 was an even bigger landslide for Roosevelt, but note that what states Hoover did win were in the Northeast.
The same was true in 1936, when FDR won all but two states: Maine and Vermont.
File:ElectoralCollege1940.svg - Wikipedia, the free encyclopedia
In 1940, Wilkie's strength, such as it was, was in the Northeast and upper Midwest.
File:ElectoralCollege1944.svg - Wikipedia, the free encyclopedia
Same pattern can be observed in 1944: Republicans strong in the Northeast and upper Midwest, Democrats in the South.
File:ElectoralCollege1948.svg - Wikipedia, the free encyclopedia
In 1948 we see the first signs of the Democrats losing their grip on the South. Truman mostly won the South and Dewey won no Southern states, but several states were peeled off by Strom Thurmond's third-party run. My guess is this had to do with Truman integrating the armed services.
File:ElectoralCollege1952.svg - Wikipedia, the free encyclopedia
File:ElectoralCollege1956.svg - Wikipedia, the free encyclopedia
Eisenhower won big both those elections, but again, such strength as the Democrat had was in the South.
File:ElectoralCollege1960.svg - Wikipedia, the free encyclopedia
1960 departed from the pattern slightly probably because the Democrats ran a charismatic candidate from the Northeast, and again a third-party run cost Kennedy a few Southern electoral votes.
http://en.wikipedia.org/wiki/File:ElectoralCollege1964.svg
In 1964, we see again an early sign of the change. It was of course a Johnson blowout, but note that of the states taken by Goldwater all but his home state was in the South -- clearly (to me anyway) the South was punishing Johnson for the Civil Rights Act.
http://en.wikipedia.org/wiki/File:ElectoralCollege1968.svg
1968 was the year of Nixon's "Southern Strategy," with the GOP for the first time deliberately trying to capitalize on Southern white voters' anger with the Democrats. It didn't altogether work -- Wallace's third party success in the South showed that while Southerners were pissed off at the Dems, they weren't ready yet to vote for the Party of Lincoln. But they would get over it.
Important point: Note that as the Republicans are gaining the South, they are also losing the Northeast and upper Midwest, their original strongholds.
1972 was such a massive tidal wave it can't tell us anything.
File:ElectoralCollege1976.svg - Wikipedia, the free encyclopedia
1976 was, I believe, the last gasp of the old voting pattern, and yet not quite: Carter won strongly in the Northeast and upper Midwest, as well as in the South.
1980 and 1984 were both such landslides that the pattern isn't visible.
File:ElectoralCollege1988.svg - Wikipedia, the free encyclopedia
1988, on the other hand, clearly shows the emerging new pattern. Note where Dukakis' strength lay: in the Northeast, the upper Midwest, and the West Coast. He lost the entire South.
File:ElectoralCollege1992.svg - Wikipedia, the free encyclopedia
File:ElectoralCollege1996.svg - Wikipedia, the free encyclopedia
I'll stop here, because by the Clinton years the new pattern was clear. The Republicans, formerly strong in the Northeast, upper Midwest, and West Coast, have ceded all those regions to the Democrats. The South, formerly a Democratic stronghold, has been taken over by the GOP.
When we have powerful a change in voting patterns, one of two things has happened. Either the character of regional politics has dramatically shifted, or else the parties have changed.
I think the latter is the more likely explanation, don't you?