I agree with the OP and RFayette's points in general. But why would northern republicans generally implement more liberal policy than southern democrats throughout the 20th century, yet southern democrat senators were to the left of northern republican senators on economics for most of that period? Most prominent southern democratic senators in that period supported New Deal or otherwise progressive economic ideas, even if they were racist to varying degrees, like Bilbo, Byrd, Johnson, etc. Why didn't that happen at the state level?
It's hard to define any dominant economic ideology of the Southern Democrats in Congress.* There was some opposition to the New Deal among Southerners in Congress, but the South had the ability to shape legislation to regional interests since the Southerners had a high level of influence over committees and the workings of the congressional majority. The prospect of redistribution between states would be attractive to a Senator from a poor Southern state hit hard by the Depression more than redistributory policies at the state level, so long as the perception was that the Federal policies would reinforce rather than upend the state's social structure in the course of relieving poverty.
*(edit: Well, that's not quite accurate. There is an ideology of support for an agricultural-based economy and low tariffs. When it comes to the level and kind of government involvement in the economy and what might be called progressive legislation it is quite variable...)