Why is "Battle Hymn of the Republic" considered to be a patriotic hymn in the United States?

“The Battle Hymn of the Republic” is far more popular today than it was during the Civil War—beloved by Northerners and Southerners, conservatives and radicals, whites and blacks. (Source)

The song became, in my opinion, a patriotic song of the United States due to the price we paid during the Civil War and the harmony the song has with the religious foundations of the nation. Historian Frank Lambert writes:

[The] significance of the Enlightenment and Deism for the birth of the American republic, and especially the relationship between church and state within it, can hardly be overstated.

While the great debate over whether or not the United States was founded as a Christian nation continues, it is nevertheless evident from our history that, like many nations before us and after, our deep devotion to God and desire to be a good people, combined with the desire for religious freedom ranking highly among the reasons for settlement of North America, has led to a strong belief that God is on our side. We fought for our freedom, under God, in our Revolutionary War. And here we were again, fighting to be free: the south for freedom to govern themselves, the north for freedom from all tyranny.

Abraham Lincoln understood the dichotomy quite well, and yet believed thoroughly in God.

The will of God prevails. In great contests each party claims to act in accordance with the will of God. Both may be, and one must be, wrong. God cannot be for and against the same thing at the same time. In the present civil war it is quite possible that God's purpose is something different from the purpose of either party -- and yet the human instrumentalities, working just as they do, are of the best adaptation to effect His purpose. I am almost ready to say that this is probably true -- that God wills this contest, and wills that it shall not end yet. By his mere great power, on the minds of the now contestants, He could have either saved or destroyed the Union without a human contest. Yet the contest began. And, having begun He could give the final victory to either side any day. Yet the contest proceeds. (Sept. 1862)

Whether intentional or not, whether inspired or not, Julia Ward Howe's Battle Hymn of the Republic struck this deep religious chord within America's soul and married it to the growing sense of disillusionment over what would be at the time one of the bloodiest wars fought by Man. This is important, for it was Americans who fought this war. Not southern terrorists. Not northern fanatics. Americans. Right or wrong, we shared both the desire to defend our homes and the desire to be right with God. And that is declared simply in scripture:

Greater love hath no man than this, that a man lay down his life for his friends. (John 15:13 KJV)

After the war, as we began to heal the wounds and reunite as a nation, with a dwindling living memory and only the bodies at Arlington National Cemetery (and others) to remind us of the price we paid to change our identity from "The United States are..." to "The United States is...", we changed the words.

As He died to make men holy, let us die to make men free

became...

As He died to make men holy, let us live to make men free

Though it may not seem that way today amidst the diversity of opinion and efforts of groups great and small to be heard, this desire to be free and our belief in a divine mandate to enjoy that freedom is quite simply the core of our patriotism, from the first landing of settlers seeking religious freedom to the last shot fired in the Civil War.

It is the “Battle Hymn’s” ability to express this sense of American mission that explains its continued prominence in times of national crisis and resolve. The song encourages us to believe still that our efforts and our militancy have been sustained for the good of some higher cause.... (Source)

Unlike "America the Beautiful," which speaks to our love for our land and "The Star-Spangled Banner," which speaks to our devotion to country, "The Battle Hymn of the Republic" speaks to the our heart and soul. Each in their turn reflects the patriotism we feel for our country — to be free, here, now.

If you look into the history of the hymn, you'll see that it was published around the time of the Civil War (to the tune of a song about the abolitionist insurrectionist John Brown). The (militant) abolitionist sentiment is clearly expressed in the original line:

As He died to make men holy, let us die to make men free

So, although I could imagine that many Christian people could sing this song and be edified, by taking the militant language allegorically, the historical origins of the hymn, and its subsequent frequent use in American patriotic contexts, creates a strong association with American patriotism.