Well stated, tilly. Though I wrote elsewhere that I was eager for the monastery to return to more on-topic material, I think this note deserves wide readership.
I think some analogies may serve to amplify your third paragraph.
- Assuming all Arabs are Muslim is like assuming all Americans are Christian. (I read somewhere that the majority of Arab Americans are Christian, though I can't vouch for that one way or the other.)
- Assuming all Muslims are radical militants is like assuming all Christians are members of the KKK.
- Assuming anyone with a dark beard or head covering is Muslim or Arab is like assuming anyone who is white is American.
Overgeneralization and ignorance are a big part of the cause of this disaster. Let's not propagate them.