Not to mention that Islamic fundamentalists worked with the Great Satan himself when they were fighting the USSR in Afghanistan.
It is quite possible to work with people you would normally prefer to see dead so long as there is one common interest overriding the differences. Case in point- the Democratic Party's willingness to work hand-in-hand with communists who would, if they ever obtained power, kill Democrats right along with Republicans, Libertarians, and anyone else who they see as a threat. And another example is Hitler working with Stalin in the early days of WW2 when those two forms of socialism - nationalist Nazisim and internationalist-communism would normally not be compatible. Yet another example is the World Council of Churches, which works hand-in-hand with atheist communism.
The desire to bring down the US is the common interest of Iraq and the fundamentalist Islamics... if they managed to succeed in it and in wiping out Israel, they would lose their common interest and then they would fight among themselves with all the vehemence they currently direct our way. But until then, we are their mutual target.