Sorry, no, the Battle Hymn of the Republic is not "neutral". It's right there in the title. Julia Ward Howe was an ardent abolitionist and the song's lyrics describe a vision of God's vengeance on the South.
They do a dis service to the hymn by not singing the 3rd verse, this hymn and its 4 verses actually tell a story and contrary to the conductor they were not neutral
Let us die to make men free is theologically correct from the New Testament. Some versions have let is live to make men free. This is wrong. The song is not talking about our soldiers dying in Battle but dying to themself, put away the flesh and accept Jesus Christ as Lord and Savior. Only then can the Holy Spirit do a work so through Him, we can save others for Christ.
But in the historical context of the song, it was written by an ardent abolitionist and suffragette, so that phrase could also mean to die to make man free from bondage. Since it was written during the conflagration of the American Civil War, giving a tune with Christian moral overtones to the Union forces to give them a reason, a powerful reason to fight and, if need be, die for. Although to the biblical scholar and devout Christian, one could say as you did, to die to themselves to put away the flesh and accept Jesus Christ as Lord and Savior to have true freedom.
