Well, maybe the song is more timeless without the Civil War verses, but in settings where I sing the song and have a chance to give a word or two of background, I leave them in, because the story adds meaning to the song, to my mind.
Especially this year, I feel the whole song, in its historical context, is most fitting for Christmas. Those two Civil War verses are not far off the mark for today!

In fact, I have toyed with the idea of changing just a few words in those two verses, to update them to the context of 9-11 and the war in Afghanistan. It wouldn't take many changes.

It's among my favorite Christmas songs, in any case.

Genie