Back on topic.
Judging from the content of the songs,
it seems like protestant Christianity.
This is of course, my opinion. I do not claim to be a professional on religion in any way. Catholics, please jump in if I'm wrong.
I don't hear any references to Saints, Mary, the Pope, Purgatory, losing salvation, the seven sacraments.
And since the recent "Nailed" is very much about Martin Luther and his departure from the Catholic church, lets go with protestantism.
As far as what denomination...that would be impossible to deduce unless they just told us. Plus it doesn't really matter. There are sooooooo many little tiny differences between all the bunches of "sects" of Protestant Christianity.
Plus they could be all from different denoms. Which would make Theocracy a giant melting pot of denominations. So let's just call it non-denominational, Protestant Christianity. ha.
But, their music is for EVERYONE!