Look at how Southerners in the House voted on NAFTA and you have your answer. The region has always been America's least protectionist.
It depends what part of the South you're talking about. The deep South tended to be more pro-trade but the upland South was more protectionist. Look at the votes on GATT, the Caribbean Trade Partnership Act, free trade with various African countries, disapproving of PNTR with China. Members of Congress from textile mill regions and Southern Appalachia voted no far more than those in the deep South.
As for 1992, I think it was a combination of:
1. General third-party weakness in the South outside of Wallace/Thurmond's explicitly southern movements.
2. Clinton and Gore were both from the South, which probably helped.