Deeply racist?  No.  Most people I've met in the South are perfectly capable of living well enough with people of other races.  But the areas I've lived in have both been a mixture of economic liberalism and social libertarianism.

It's, of course, going to depend on where you visit.  But, in my experience, you can find ignorant people anywhere.  If it's not racism, it's xenophobia, or anti-intellectualism, or simply general anti-"Frenchie-ness".  I don't think the region is deeply racist.  Are there tensions?  No doubt about it.  But it's not nearly as much of an issue today as it was back in the mid-20th Century.

Be nice to America. Or we'll bring democracy to your country.