The reason for the controversy is that the song was written during the Civil War-era, advocates secession, and uses (really) disparaging language to refer to the North. (You can read the lyrics yourself here.)
Why the fuss about something that most people don't even know exists? That would be a good question to raise with our students. Ask them to read the lyrics for your state song. Ask them to speculate when it was written. (This would be a good opportunity to practice looking for contextual clues.) Ask them, are there any images or phrases that some people today would find offensive? This will give you the chance to connect the song lyrics (a primary source), to the historical period in which it was adopted, to current attitudes.
This link takes you to the lyrics for all 50 states.