What percentage of the white population of the South was in no way connected with slavery?

It is difficult to provide an exact percentage, but it is likely that a significant majority of the white population in the South had some connection to slavery, either directly as slave owners or indirectly through economic, social, or political ties to the institution. The Southern economy and society were heavily dependent on slavery, so it would have been rare for white Southerners to be completely disconnected from it.