I'm sorry to be late to this thread, but 20 years ago, an Arlington (VA) bluegrass station DJ did some research on this. The music is definitely the same as Ireland's legendary "Kevin Barry" song, which is a tribute to an 18-year-old rebel who was hanged by the British when he refused to inform on his fellow rebels. The words are completely different, however. Lots of artists recorded this song (including the Clancy Brothers). Lonnie Dunnigan's version is particularly good.

Not too long after Kevin Barry became popular, several Irish singers used the indentical music (but different words) for the song, "Will My Soul Pass Through Old Ireland." I was unaware of the McSwiney connection.

The words of Charlie Moore's American version are eerily similar to the Irish ones and, to me at least, there is little doubt that Moore simply changed a few of them, while keeping the music from the original Kevin Barry song.

I'm a Civil War junkie, including music, and I have come up with zero evidence that The Rebel Soldier even existed in the 1860s, and was not heard in America until the late Charlie Moore first recorded it in the 1970s. His version is good, but not as good as that of The Country Gentlemen. Jimmy Arnold also recorded a nice version.

Incidentally, the Kingston Trio's popular song, "Tom Dooley" first appeared shortly after the Civil War ended. Its music was harsher than that of the trio's and the words slightly different. It was called "Tom Dula."

Finally, the beautiful "Ashogan Farewell" song that became the theme music of Ken Burns' remarkable TV series on the Civil War was first heard in America at a fiddle contest in upstate New York in the 1970s.
The best version of this that I've heard is by the great Irish flautist, James Galway, paired with pianist Philip Coulter.