If I have to be completely honest I don't believe these people can live in peace. They will always find some reason to divide each other into groups, be it slightly different religion or whatever, and then start fighting. Obviously not everyone is like that, and I doubt the everyday citizen knocks on doors and shoots people in the head, but there are just too many extremists.
Disagree - Yes, people will always have disagreements, but the nature of the disagreement is fundamental.
The only thing that can convince people they're actually doing the world a favor when they're voluntarily participating in a war is religion.
There's simply no other kind of political extremism of extremism of any kind that is capable of the same thing.
Exceptions may be single occurrences like mass-murders by a single person or a small group, but that sort of terrorism exists on an insignificantly tiny scale and has more to do with the mental health of the individuals involved.
Agree - No, these people can't live in peace because there's nothing on earth that could change their mind. The only way they could be at peace is when every single last person on Earth praises Allah. I also agree that they're barbaric, unintelligent and violent enough to still cause problems in a society without extremist religion, but again, the terrorism would exist on a much smaller scale.
I personally think we should intervene, but in the smartest way possible.
Cost effectiveness isn't really in any military's book, let alone the USA's military.
I'm not nearly informed enough to confidently state what approach should be used, but I don't think mercy should be a high priority.
One could argue that fighting militant extremists really only makes the issue worse, because you're giving muslims all the more reason to pick up a weapon and fight. I'm not sure if this is correct, but it's definitely something that should be considered.
Understand that the Islam is likely to be the biggest problem of the 21st century.
Check out that sick hardscoping filth at 29:30