It’s certainly a minority, but there are pockets around the world where the numbers are big. Look at some of the Mormon sects in America. The majority are lovely, normal, people, and then there are extremes examples where people live on closed campuses basically, girls are married off to polygamist men as young teenagers and some of the teenage boys are cast out. Or, other Christians who try to change laws to control society so people will follow the dictates of their brand of Christianity. I guess you aren’t counting things like some Orthodox Jews who only really try to control their family and there is peer pressure in the group. They use shunning and ostracizing and pressure to control their children, wives, neighbors, but they do not try control greater society. Not all orthodox do what I named, just some sects. The Amish are similar.
The Muslims, all I know is most Muslims I know in America are very nice, educated, normal, Americans. There also seems to be plenty of countries with Muslims that are peaceful and women are educated and westernized. But, there is a very large number of theocracy governments run Muslims and groups of Muslims popping up that they are wreaking some havoc. They are a minority among the many muslims in the world, but they still have a real presence.
America continues to be allies with countries who seem to support extremism to some level. Other western countries too. The old the enemy if my enemy is my friend and dependence on oil doesn’t help. It’s pretty annoying.
In your own country, Ireland, all that crazy fighting between the Protestants and the Catholics for years. That was some crazy terrorist stuff. It wasn’t too long ago. You still have public schools run by religions as far as I know (correct me if I’m wrong). Plenty of people in America would like to have government funded religious schools here, but luckily we have resisted that route.