Welcome, godless Marxist.
There is no cognitive dissonance involved. The faithful of two mutually exclusive religions naturally are going to be at odds with each other. Modern leftist nonsense about "Abrahamic religions" aside, there is nothing shared between Christianity and Islam. Muslims are paynims who seek to destroy Christendom, and you somehow think Christians should support that?
The only questionable thinking here is how you could possibly support evil attacking good because good fights back against evil. If you see good and evil as morally equal and equally valid, then the problem is with you and your godless thinking. I am assuming you do not even understand that Islam has been violently expanding since its founding, or that most of the Middle East were Christian lands for centuries before they were violently subdued by the paynims.