The battle is between terrorism and tolerance, between violence and peace, within each culture. It's amazingly symmetrical between Christians and Muslims, where the most dangerous people pick a few passages out of an ancient book and represent them as key to their holy war.
As someone without roots in either Christianity or Islam living in Texas, guess which bunch of extremists I find myself more afraid of on a day to day basis?
Angry people who take ancient books too seriously are dangerous. That's surely true. But it really doesn't matter much which book they are worked up about.
The way to fight them is not by mistreating all their distant relatives just because of their culture and background.
My grandfather ended up in Hitler's gas chambers because of thinking like this. When you think of "Muslims" as the enemy you are no better than someone who thinks of "Jews'" or "Christians" as the enemy. All of us have good sensible people and terrible, evil people among us. The question is which tendency we want to celebrate.
When you buy into an enemy extremist's view of what their culture is about, you are doing them a huge favor. Is that really what you want?
The way to fight extreme intolerance is with extreme tolerance. "Fighting fire with fire" actually is not the strategy of most fire departments.