The fact is that while Union armies did occasionally "live off the land", Confederate armies did so constantly.
Yes, within the Confederacy they did usually pretend to "pay for" their "requisitions", but once outside the Confederacy they considered any & all Union properties theirs for the taking, sometimes using Confederate money to "pay", but more often not.
By war's end, Confederate armies had invaded or raided into every Union state & territory they could reach, including: Maryland, Pennsylvania, Ohio, Indiana, Kentucky, Missouri, Kansas, Oklahoma and New Mexico.
Confederate guerillas also operated in California, Colorado and even Vermont.
In every case they left a trail of destruction and seized "contraband", including "recovery" of any runaway slaves they could grab.
But in proper historical perspective, the US Civil War was absolutely one of the most "civil" of civil wars ever, with relatively few civilian massacres, deaths, mass starvations, etc.
Both sides considered themselves, and generally behaved as Christian soldiers.
While it may be true, and i don’t know that it is, that Confederate soldiers, acting independently or in small groups, committed crimes against civilians, it wasn’t a matter of sanctioned national policy, as it was in the Union army of terror.