I think it is a safe statement that there is broad (overwhelming) agreement among historians that this just isn't how the history of the parties has gone. Political scientists recognize 5 (or more) "
systems" to describe the party alignments. Each system was dominated by different issues and did not have a very strong relationship to the prior alignment. The parties in the 1860's bear no relationship to today's -- as late as the 1920's there is still probably little or no relationship.
The coalitions of voters that grouped along those issue lines resemble today's (with the labels flip-flopped) in some ways: the Republican base was more urban, industrial and the "lenders" in the financial sector, the Democratic base was more rural, agricultural and "debtors."
I'm sure endless PhDs have been written to explain why the Great Flip-flop happened. The Democratic party during the New Deal was an unstable coalition between two mismatched, even adversarial interest groups, and eventually they would have been cleaved apart. The civil rights movement was what historically split them, but it was only a matter of time, and it didn't need to be about race at all.
If you want to see one difference, look at attitudes towards federalism. The Republicans were strongly federal -- strong enough to go to war to hold the union together. The Democrats were strongly confederal -- strong enough to claim to right to secede. Today, the party attitudes are exactly the opposite.
All institutions try to trace back to their Founders to claim additional legitimacy, but in this case neither the Republicans' claims to be the Party of Lincoln nor the Democrats' to be the Party of Jefferson hold any water.
