Yes, but let's be clear here. It was not so much that there was scriptural warrant for individual Christians on their own initiative, or for the church as an ecclesiastical body, to undertake the liberation of Christian victims of Islamic aggression. There is no such scriptural warrant. What there IS scriptural warrant for is for governments to protect the innocent from aggression, and if necessary to wage just war to do this. The Christians in the Middle East became victims of Islamic aggression in the first place and in large part due to the failure of their governing authorities to do what they were supposed to do (per scriptural warrant) to defend them. The case for other governments to later intervene in their behalf, roll back the Islamic aggression, and liberate the oppressed Christians, is less clear, but perhaps could be made on the basis of a just war ethic. But the ONLY scriptural warrant for such an action is if the action is initiated by GOVERNMENTS, and is entirely a GOVERNMENTAL action. Christians can certainly support and participate in such an action, but because they are citizens, not so much because they are Christian.
It was the failure to properly define the line of authority between the church and the state that was at the root of whatever problems occured with the Crusades. This, at its root, was due to a failure both of people running the church and people running the government to obey the clear teachings of scripture, which gets back to my original point: Any criticism of the behavior of Christians during the crusades must be based on the fact that such behavior was out of DISOBEDIENCE to the scriptures, rather than out of obedience to any scriptural commands.
It was the failure to properly define the line of authority between the church and the state
That "line" was fuzzy indeed a millennium ago. I agree, though, that the failures of the Crusades were in large part a result of "DISOBEDIENCE to the scriptures", and forgetting the nature of the mission.