The Church has military orders and such, but hardly ever uses it or uses it in conjunction to temporal rulers on limited basis. Essentially the reasonable authority figure of the setting with a rather large stick.
Members of the Church carry symbolic weapons and train in martial arts as a reminder of their struggle against their lower nature.
Our Lady of Badass was founded by a former Badass Preacher who defected from a more peaceable church, and created an organization of fighting clergy to protect the masses from a rising ancient evil. Robert is the latest of The Chosen Many.
The Church doubles as a military force (especially when it comes to fighting the Legions of Hell).
They worship a War God, who demands battlefield sacrifice and accepts only those who die by the sword into Warrior Heaven.
They are from a sect that was once the victim of persecution and does not intend to be so again.
The Church serves a community on a bloodstained frontier between two rival Empires. War is a necessary part of survival and the Church's practices will reflect it.
Inverted: Robert is a warrior for The Enlightenment, a brotherhood of militant atheists who seek out and destroy all traces of religion.
Subverted: Father Robert is an elderly priest who preaches peace.
Double Subverted: But when the Legions of Hell knock at his door, he also turns-out to be a Badass Grandpa.
Conversed: "Father Robert sure fights a lot on this show, being a priest and all".
Deconstructed: Robert gets kicked out of the church when his fellows deem his methods too violent.
Reconstructed: Robert comes up against a review panel of bishops, furious at what he's done, but he defends his actions with scripture on the subject of acceptable violence, and talks several of them round to his side. They have no choice but to throw him out of the church, but they suggest he continue his work as a Cowboy Preacher.