I would disagree that "I Sang Dixie" mourns either the loss of Southern values or the loss of the Confederacy.

If you listen to it carefully with an open mind (which I hope Mudcatters can do)--especially when sung by Dwight Yoakum-, it seems clear it's about the loss of a man who did identify with the South.   But the protagonist mourns the death of that man--dying far from his home--not any "Lost Cause" regrets.