The modern day Conservative is the equivalent of a Dixiecrat?

The modern day conservative has no equivalent. White conservatives who believe in small government and personal freedom are stuck voting for Republicans because they can't bring themselves to vote for anything progressive. Minority conservatives that are generally ignored by Republicans and turned off by their racism by association vote for Democrats because at least they give them lip service.

And the party of Lincoln was much closer to FDR than a lot of people want to believe. There's no way Lincoln would be considered a conservative much less a Republican now. So they still weren't "right" by Gadwall's standard.