First: you need to realize that ISIS is a minority group, an extremely weak military force, and someone whose tactics rely on us turning fear and hatred into recruitment tools. They want us to turn on the refugees coming from Syria, because they want them to feel like their only option is to become a terrorist, because all the West wants to do is drop bombs on their country and hope the problem goes away. The fact that we are even considering "dropping our morals" is proof that their tactics are, indeed, affecting people.

Second: Hiroshima and Nagasaki wasn't a situation where we needed to drop our morals. We had crushed Japan militarily, and the only ones that truly supported further war were the military brass angry over their toys being broken. The Japanese government reached out diplomatically, and we refused repeatedly. We didn't want the Russians sharing Japan with us, so we decided to nuke them. We dropped pamphlets about evacuating cities due to atomic bombs after we nuked two cities, not as a warning, but as a threat. It was a senseless action done as a way of flexing our muscles, it saved no one, killed tens of thousands and irradiated two cities.

Third: yes. Barring people who are escaping persecution from a rebel force which we helped arm (because these rebels are the same ones that the US armed a few years ago) just because the monster we created might possibly sneak in is, in fact, morally wrong. Turning a blind eye to the genocide of the Assyrians and the steady downslide of human rights and livability in the region as we proceed to drop more bombs is, indeed, morally wrong. Assuming that every single refugee coming into other countries is a terrorist because of a piece of propaganda released by a paper tiger so desperate for manpower and resources that they recently resorted to strapping IEDs to chickens is stupid. It's also morally wrong.