You may be forgeting that we have been sending Christian missionaries to the Middle East and other Muslim countries for a couple of centuries for exactly the same reason... we think those people are heathens who need to be saved. Islam has no corner on the market for religious extremism, nor harsh prejudice against non-believers.
We have also been exploiting their resources, primarily oil from the Middle East, while supporting various repressive governments whose only good points were that they protected our economic interests. Our primary ally in the Middle East is Saudi Arabia, where much support for Sunni extremism is funded, while we focus on fighting Iran whose Shitte population hasn't brought a single terrorist operation into Europe or the US. The ISIS extremists are Sunni, but we know so little about their religion that we think they are all the same.
Making this a religious war will be a huge mistake. Something like that can't end, and we will diminish ourselves by trying to simply frame Islam as the problem here. We have to look more broadly for solutions than that, and alienating a huge population of people based on their religious beliefs is completely the opposite of what America has stood for.
Meanwhile, there is the question of practicality. Can someone please give me examples of the kind of screening questions we will ask at US entry points that will identify a Muslim? Should we just offer everyone a ham sandwich and arrest the ones that refuse?