The U.S. went to Iraq with U.N. Security Council resolutions. Not votes of the General Assembly.
It has very little or nothing to do with religion. Israel is a long time U.S. ally, dating back to the Cold War. The enemies of Israel are in large part the enemies of the United States. The U.S. has no sympathy for Hamas or Hezbollah. Anything Israel does to weaken these entities will be supported by the U.S. The issue is civilian deaths, which the U.S. has pushed Israel to try harder to avoid.
As I said, the U.S. support for Israel is based on foreign policy pragmatism much more than any religious concern.
What pragmatism? The fact that they are also enemies of Hamas and Hezbollah? Both of these groups were formed in 80's in response to Israeli occupation. Religion does play a role look at Christian zionist groups and the role of Dispensationalism.