There were several hundred thousand white Southern Union soldiers but they get nowhere the attention as the dubious speculation over the existence of a handful of black Confederate soldiers. The Lost Cause myth of a united Solid South is as persistent as it is misleading.
There were entire communities in the South that remained loyal to the North and, similarly, there were entire communities in the North (especially in Pennsylvania but even as far north as Vermont) that were loyal to the South. This is all well-known to historians, and interested non-historians like myself.