The Democrats were definitely weak on race issues before the 60s and Republicans were able to hold onto a lot of the African American vote from the time of Lincoln up to the 60s.

But the Democrats were also the party of the New Deal. We got Social Security and Welfare from the Democrats back under FDR. To say the Democrats were the party of big business and conservatism compared to the GOP isn't quite right. The Democrats had a fairly populist portfolio of voters, many of whom were agricultural. Farmers from the south would be reliably Democratic and not exactly be bleeding heart liberals when it came to anything other than farming subsidies. Both parties have always had their portfolio of corporate backers. Noam Chomsky was talking about this in some detail once, but I don't remember the specifics of which corporations were backing FDR vs. the GOP.

From what I have read, Nixon had a fairly respectable record on segregation and discrimination before he embraced the Southern Strategy. It makes the betrayal even more painful to think about.