One thing to keep in mind is that the left-right divide takes different forms in different places, and if you are thinking of a traditional economic leftism, that is by no means incompatible with conservatism.

It's a bit of a different context, but in England, the origins of the conservative movement were in attempts to protect the social status quo against liberal capitalism[0]. You can see the same tendency in Spanish or rural Russian Anarchism - farmers wished, quite reasonably, to preserve the social and economic relations that they depended upon against the instability of modernization. The difference is in what allies they sought, and how they articulated their position.

Conservatives typically sought to form a coalition of the rural gentry and the rural peasantry, and to preserve the social relations first, and the economic relations second.

Anarchists typically sought to form a coaltion of the peasants and urban workers, and to preserve the economic relations ('land redistribution'), but were typically less interested in the social relations.

If you apply this perspective to the Democrats and the Republicans, you can see why the Republicans come out easily ahead, without any shifts in the politics of rural Americans. Both parties are economically liberal, but by appearing to safeguard traditional social relations, and by associating themselves heavily with decentralization and federalism, the Republicans come out well ahead.

[0]: Raymond Williams, The Country and the City.