The religious group, the Faith of the Seven and their extremist militant branch, the Faith Militant - or, the Sparrows - in Game of Thrones are certainly terrifying in the means and pace of which they've risen to power, as well as their stringent views towards religious practice, law, and punishment.
While the Sparrows could represent any number of religious groups, their ability to use force and strategy to usurp the political position of their spiritual predecessor was inspired by just one religion and one period of time.
According to author George RR Martin in an interview with EW, the religious group that has taken King's Landing by storm was inspired by the Catholic Church in medieval times:
The Sparrows are my version of the medieval Catholic Church, with its own fantasy twist. If you look at the history of the church in the Middle Ages, you had periods where you had very worldly and corrupt popes and bishops. People who were not spiritual, but were politicians. They were playing their own version of the game of thrones, and they were in bed with the kings and the lords. But you also had periods of religious revival or reform—the greatest of them being the Protestant Reformation, which led to the splitting of the church—where there were two or three rival popes each denouncing the other as legitimate. That’s what you’re seeing here in Westeros.
The two previous High Septons we’ve seen, the first was very corrupt in his own way, and he was torn apart by the mob during the food riots [in season 2]. The one Tyrion appoints in his stead is less corrupt but is ineffectual and doesn’t make any waves. Cersei distrusts him because Tyrion appointed him. So now she has to deal with a militant and aggressive Protestant Reformation, if you will, that’s determined to resurrect a faith that was destroyed centuries ago by the Targaryens.
Acting as a policing power and political play between the religious leaders and the throne aren't the only things the Sparrows have in common with the medieval Catholic Church. It also inspired the fictitious church in other ways:
Instead of the Trinity of the Catholic Church, you have the Seven, where there is one god with seven aspects. In Catholicism, you have three aspects—the Father, the Son and the Holy Ghost. I remember as a kid, I was always confused by that. ‘So there are three gods?’ No, one god, but with three aspects. I was still confused: ‘So he’s his own father and own son?’
Like I said before, I think almost any extremist religious group could resemble the Sparrows at some capacity, but it's definitely interesting to hear what ideology directly inspired George RR Martin to bring aspects of their history into the fantastical world of Game of Thrones!