Southern Dems at least since the days of Wilson were some of the loudest voices for internationalism and foreign interventionism with some obvious exceptions including Senator Reynolds of North Carolina. Along with some ex-Socialists, they formed the basis of the neoconservative movement that would help bring Reagan into office.
Wallace's foreign policy reminded me a lot of Trump's. Stay out of foreign entanglements unless you're sure of victory, then go all in.
Wallace had more of a "Jacksonian" foreign policy, which befit his largely up country South base.
Coincidentally, in the South, Trump shares largely the same base of support.
Many of these same areas saw Democratic gains or solid holds in 2006 against Bush era Republicanism.
What sort of foreign policy did “down country” Southern politicians favor?
Its generally referred to as "Low Country", but militantly anti-communist for one. If the poster boy for the up country "rogue Democrat" is Wallace, than that of the Low Country is Strom Thurmond. Thurmond was a Republican by 1968 and supported Nixon as did much of the low country and Southern middle class/suburban vote.
The dividing line between Wilsonian and Jacksonian can get rather fuzzy, especially in terms of willingness to fight a war. The differences are the motivations for doing so, and the appetite for a long term conflict/occupation.
Jacksonians would have been all in on retaliation after 911, but would have soured on Bush as Iraq dragged on and the motivations became less clear. The idealistic Wilsonian justifications about spreading Democracy and "at least we got rid of a brutal dictator would not have much appeal to Jacksonians at all. It is at this point that Anti-War politics gains steam in the region. You saw this in Vietnam in parts of Kentucky, Tennessee and Arkansas. This is why Nixon, with his outer-South strategy had to pull off a delicate balancing act between promising to end the war and not allowing America to lose to the Commies. You also saw temporary surges of support for Dewey in 1944 in places like Tennessee that did not carry over to 1948 at all.