If we're talking rednecks like people who live over multiple generations in small towns or rural areas generally, and that comes out in their cultural preferences, for Asians (and I'm counting Indians) you're for sure gonna need changes. Asian farmers and rural laborers were very important for Hawaii but you could argue the islands are too small to foster an insular "redneck" culture; in larger states like California, the government resisted Japanese land ownership right up until Internment. After Hart Celler you still had people coming seeking land, but visa programs and such have skewed the demographic more toward people who, rich or poor, see their future in the cities.
So in a way, if the laws were less (making Asian land ownership easier) and more (restricting immigration generally, but not distinguishing by occupation) discriminatory you'd probably get a distinct class of rural Asians in the West. If you want them in the South though, I think the window for coming in/getting land/putting down roots is kinda closed after the Cotton Era, but there might be a second window around Reconstruction. That's when you could have Asians carving out a niche amid the New South.