http://grantland.com/hollywood-prospectus/ask-the-maester-the-tale-of-brave-ser-barristan-the-faith-militant-and-the-fighting-harpies/

"The Faith Militant is a loose affiliation of religious fanatics who are pledged to protect the Faith. The Faith Militant is organized into two orders: the Poor Fellows, drawn from the peasantry, and the Warrior’s Sons, former nobles and landed knights (like Lancel Lannister) who gave up their worldly possessions to serve the Faith. They are somewhat analogous to the Knights Templar and Hospitaller of the Crusader age, acting as the sword arm for their religion."


The show hasn't really established just how much power they have, but it's reasonable to assume that they have the numbers and the motives (devout fanaticism) to carry out their intentions.