The Faith Militant is made up of two orders, the Warrior's Sons (nobles, lesser sons of great houses who renounce their fortunes and devote their lives to defending the Faith, much like the Kingsguard), and the Poor Fellows (commoners who vouch to do the same, women can be accepted into this order).
After Aegon I's conquest, the Faith still wielded these powers and as such, even he had to placate them. They are afraid of his dragons but nonetheless look on with disdain the Targaryen incestuous marriage practice. After Aegon died, they openly revolted when his son Aenys married his own son and daughter, and the revolt lasted for 7 years, 1 under Aenys's short rule and 6 under his brother Maegor the Cruel. The latter was especially brutal in his treatment of the rebellion, placing a weapon ban on any member of the Faith and put a bounty on the head of every rebels (a Dragon for a Warrior's son, a stag for a poor fellow and a penny for a female poor fellow iirc). The rebellion only ended with the death of Maegor and his nephew Jaehaerys's ascension, who pardoned the rebellion at the conditions that while the Faith doesn't need to approve of the Targaryen's practice, they need to acknowledge them, and the dissolution of the orders.
Fast forward 250 years and King's Landing under Cersei's rule was a shit show. The War of the Five Kings ravaged the land and drove the common folks to the big cities scavenging for sustenance. The Iron Throne, at this time, was neck deep in debt and owed a million dragons to the Faith. After Cersei's killed the High Septon, who she in her paranoia think assisted Tyrion's escape and know about her incestuous relationships (Jaime, Lancel), the Sparrows (zealot common folks) stormed Baelor's Sept and forced the Most Devouts to elect the High Sparrow the new High Septon. When Cersei's came to him to suggest that he forgive the crown's debt, he refused, but suggest an exchange, the reformation of the orders for the debt. In her stupidity, Cersei agreed to it and then she had a fighting force largely outnumbered what's at her disposal (Lannister's personal guards and the City's Watch, some 2000 strong) inside King's Landing, with Jaime and the Lannister fighting forces off to subdue the Riverlands and the Tyrells under Mace Tyrell sieging Storm's End and Dragonstone.
And yes, I remember all of that. FML.