Actually, I think the First Crusade was justified, to repel Muslim military invasion. However, the Crusades quickly went off the rails, and were ruthlessly conducted.
i) Although Urban II called upon the Franks to wage a counteroffensive against Muslim aggression, it's not as if "the church" led the military campaign. The pope, cardinals, bishops, and priests weren't combatants, although there was a military order of monks (Templars).
All Urban II could do was urge the "civil ruling authorities" to repel Muslim invasion. Are you saying religious leaders should never give civilian leaders advice?
ii) Muslims were killing and enslaving Catholics. Didn't a medieval pope have a right to urge civilian authorities to protect Catholics? I'm not Catholic, but I'm just discussing the issue in terms of how the table was set in the middle ages.
iii) Where's the line between "the church" and civilians? Almost all civilians in the Western Roman empire were Catholic.
iv) There is a tradition the men of the cloth should never take up arms. Do you agree with that? If a violent man storms into a Sunday school and threatens to kill the children, doesn't the pastor have duty to prevent a massacre by using lethal force, if necessary, to ward off the assailant?
v) The appeal to Rom 13 is fallacious. To say civil authorities have a role in military action doesn't say anything about the role of the church one way or the other.
vi) There are multiple justifications given for the Crusades. We don't have to accept the justifications offered by Urban II to say the Crusades were justifiable in principle as an act of self-defense. We're not bound by Urban II's rationale. We can have independent reasons for believing it was necessary to repel Muslim military aggression.
vii) I agree with your larger point that Europeans make a basic mistake when they treat Roman Catholicism as their default representative of Christianity.