Muslims are not a single group with consistent values and behaviour, just as Christians aren't a single group with consistent values and behaviour.  Every religion has its members who go to far, who accept violence as an acceptable solution to problems, who treat people who don't share their values as evil.

Don't kid yourself by pretending otherwise. There have been plenty of LGBT people beaten and murdered in North America by Christians. Women are raped and abused in our culture just like they are in their culture. Where I see a difference is that many muslims live in third-world conditions under oppressive regimes where archaic values are maintained rather than marginalized as they have been here.  Under those conditions, backwards practices dominate, like they do in many parts of the Third World.

The problem with preventing terrorism is ultimately the same as preventing any other kind of murder: how do you do it?