You can't attach and detach things to Islam for convenience sake. Islam isn't Mr. Potato Head.
If a liberal took this stance it would be "political correctness run amok". I'm sorry that Al Qaeda doesn't have a capital, a uniform, a flag, or other face discernable from the rest of Islam, but Islam is not the face of terrorism. If people can't think beyond generalizations there is no reaching them.
I don't think we should enable people's ignorance. Just because people don't understand the reality doesn't mean that they should be bargained with or capitulated to. Sure, we can all understand their reaction, but that doesn't mean it should be condoned. Islam isn't the enemy, yet people certainly are acting as if it were since this became the wedge issue of 2010.