We probably care because they are blowing things up, setting things on fire, killing people, and generally causing mayhem.
Just a wild-as-hell stab in the dark.
My point, when I ask "why do we care what their religion is", is threefold.
1. It implies that crazy Muslim radicals can be reasoned with, "if only we just understood them a little better". This is obviously not the case, as their entire worldview is comically devoid of reason.
2. Even if we were to "understand" them, crazy Muslim radicals demand that we do ludicrous things like force women to cover up, never drink and never eat bacon. I'd rather throw acid in my own face and stone myself to death before I did that. Live Free or Die. USA #1.
3. As soon as you initiate violence, you lose your right to be understood. Terrorist, meet drone, gg.
Re: what makes a terrorist
I'm not an expert. My personal belief is that it's a lot like gangs. Young men, poor, disenchanted and constantly humiliated are preyed upon by religious fundamentalists that give them self-respect, community and status. I think it's worse in Islamic countries because, as many have pointed out here, a lot of those countries are theocracies so you can go a lot further down the crazy road before anyone notices a problem. There's a very fine line between being a "good Muslim" and a "sexist, abusive, murdering asshole", and there's not a lot of guidance away from violence in those cultures.
In that vein, I'm guessing the solution is economic development (private enterprise), cultural & religious liberalism, and a strong, secular, law-bound police force. All the things the US tries to promote and organizations like the Taliban and Al-Qaeda oppose, coincidentally.... Hearts & minds guys, hearts & minds.
Re: fundamentalism & religion
Fundamentalism is always dangerous, because fundamentalists can't be reasoned with. They're like the zombie horde of Jesus/Allah/Spaghetti. That's why I usually separate them out from other practitioners, because I actually separate them out from the entire human race.
I think characterizing a religion by its followers is an imperfect measure. People in the US South raped and whipped slaves to death while reciting scripture. On the other hand, Christian charities rival the US in terms of aid given to poor, struggling regions when you factor in manpower.
What I mean when I say, "it's a mistake to characterize a religion by its radical members" is that you shouldn't look at the 1st generation Pakistani family down the street and assume they're terrorists because of what you saw on the news about radical Muslims. The vast majority of Muslims, just like the vast majority of everybody, are good, reasonable people.
That's not to say that a lot of them don't have stupid ideas. Sharia law's views on dress, marriage, sex, inheritance, etc. are goddamn retarded. But a lot of Muslims are still 1st generation immigrants and they don't really know anything else, and it's also worth saying that the US had similar problems when it was still accepting huge amounts of European immigrants in the late 18th, 19th and early 20th centuries. Stuff like this improves over time as people from countries that regularly gas thousands of people for having the wrong color of clothes gradually come to realize that was hellish and they didn't deserve it, and they certainly don't have to perpetuate it. Kids generally help with this :).
Of course, a large barrier to acculturation is xenophobia. When you have large portions of bigoted, white society denying entry to immigrants, what you end up with are barrios, chinatowns, ghettos, etc. Then these idiots point to what they created and say, "SEE?!?! WE TOLD YOU THEY WERE SUBHUMAN." Ugh. Indeed stupidity is found in all cultures.
You know I agree that deliberately trying to piss people off generally doesn't help anything. On the other hand, I can understand people being upset because it seems like A FUCKIN YOUTUBE VIDEO IS AN EXCUSE TO SET EVERYTHING ON FIRE. The immediate reaction from all the news I watched (and I watch a lot of news) was, "wow, look at the HORRIFYING, TERRIBLE, AMAZING POWER OF YOUTUBE, WE REALLY NEED SOME WAY TO REIGN THAT IN". There's also a movement to try and get people to stop offending Muslims by not posting YouTube videos or not printing offensive cartoons or not putting up ads in subways. No. What we need to reign in is violence, not speech. Live Free or Die. USA #1.