It's not incorrect, even at its most basic Catholics are Christians therefore the Crusades were fought by Christians and it it misrepresentative to suggest the Catholics are not Christians.
At a more complex level, the Crusaders were made up of predominantly the Latin (or Western) Christendom and while the Papacy held hegemony in Western Christendom it was not complete. Also until the Fourth Crusade the Western and Eastern Christian Churches were unified (Known as Universal Christendom) and both fought in the early Crusades (it was at the behest of the Eastern Orthodox that Latin Christianity pursued the First Crusade) although as I said, Christian did fight Christian as well as Muslim and Jew, particularly in Outremer and during the Fourth Crusade and the sack of Constantinople. The truth is that Christendom included the Latin and Orthodox churches as well as Western Europe Christian Nation States and Eastern Nationalist Orthodox Churches. Simply because the Papacy was at the height of its socio-political power during this period shouldn't give the impression that Catholicism was either not Christian or didn't hold authority over Western Christianity (one of the reasons why Pope Urban II declared Crusade was to initiate primacy of the Latin Church over The Christian States and the Franks).
Whether you like it or not, The Crusaders were Christian.