It's a common misconception that the crusades were a crime of white christians versus non-white non-christians. In reality crusades were just as well a crime against other white christians as against non-white christians, white non-christians, non-white non-christians, an excuse would be found for any of these targets
Oh yes that was surely a motivator for some but also an excuse for others.
The political landscape of that time was truly complicated and chaotic in a way that is hard to truly capture in the image we have of that time period brought through general education, mostly because of lack of time to explain it all properly
