You were right, McSteamy, the song deals with war but, more importantly, also with the perception of war, with the doctrines that are grafted into the national corpus, so that the people do not look upon the series of murders as which war can be apprehended but upon its ideologic superstructure. Thus it happened to the speaker:

I's taught and brought up there
The laws to abide
And that land that I live in
Has God on its side.
(First stanza)

The two latter lines, like those of the following six stanzas, refer to a religiously soaked national identity that, still descending from the pilgrims, survived through the times and the battles against reason until the present day. This belief that god were blessing the American nation, that its actions were in accordance with his will manifests itself in the perception of the wars it has fought, beginning, in this case, with the indian genocide:

The cavalries charged
The Indians died
Oh the country was young
With God on its side.
(Second stanza)

It was murder: but the young nation had god on its side. From a war certainly not glorious but indispensable nontheless in the second stanza, we are coming to a magnificent one: The soldiers are historic heroes for schoolchildren:

And the names of the heroes
I's made to memorize
With guns in their hands
And God on their side.
(Third stanza)

Now the facade gets chapped:

The First World War, boys
It came and it went
The reason for fighting
I never did get
(Fourth stanza)

Suddenly there is a great war that is lacking both necessity and glory. The speaker, however, bethinks of the national bearing, of the zeitgeist as well:

But I learned to accept it
Accept it with pride
For you don't count the dead
When God's on your side.
(Fourth stanza)

But then there is the Second World War. The Germans have murdered millions of people, half of Europe lies in ruin and ashes:

When the Second World War
Came to an end
We forgave the Germans
And we were friends
Though they murdered six million
In the ovens they fried
The Germans now too
Have God on their side.
(Fifth stanza)

The speaker does no longer understand how anyone can forgive the horrors of war. Ironically, he concludes that now god must also be on their side, for they have murdered like the Americans before them, on whose side god, of course, has always remained.

Thereafter, we hear two stanzas on the (then-present) political situation:

I've learned to hate Russians
All through my whole life
If another war starts
It's them we must fight
To hate them and fear them
To run and to hide
(Sixth stanza)

But now we got weapons
Of the chemical dust
If fire them we're forced to
Then fire them we must
One push of the button
And a shot the world wide
(Seventh stanza)

These stanzas, though, end as follows, as if the speaker puts his blinders on again:

And accept it all bravely
With God on my side.
(Sixth stanza)

And you never ask questions
When God's on your side.
(Seventh stanza)

In the following eighth stanza, we can eventually hear of the conflict between reason and doctrine that takes place within the speaker's mind:

In a many dark hour
I've been thinkin' about this
That Jesus Christ
Was betrayed by a kiss
But I can't think for you
You'll have to decide
Whether Judas Iscariot
Had God on his side.
(Eighth stanza)

It is as the four latter lines say: You will have to decide.

The speaker's final words are simple, but we have heard of the long way he has walked in the footprints of his forbears, and we think, since we always side with reason, that now the nation shall follow in his steps:

If God's on our side
He'll stop the next war.
(Ninth stanza)

Now we know that lyrics can matter.