Of course Al Quaeda and the American military are infused with religious beliefs.
Most wars can be reduced to religious conflict and yes they are exacerbated by malicious politicians and outsiders but they still wouldn't be there if there wasn't the division of religious belief, at least not through the channel of religion. People might find something else to fight about.

Religion states unequivocally that a loyalty to one necessitates that other religions are not acceptable. For example, if a Catholic were not so sure of his/her religion then it would be O.K. for him/her to be Jewish, Protestant, Muslim or fill in the blanks. Show me the evidence that religious people think all religions are equal?

If that were the case, then who would need them?