The reason I suggest a focus on the medieval timeframe is because it is very easy to fill the thread with contemporary references, and there is no shortage of such threads.
But if you insist, it is my opinion that the present unpleasantness is fundamentally different from the Crusades. The leaders of the War on Terror are very specific in shunning a Christians Against the Islam designation; Jerusalem is not the stated objective; there is no popular upswell of support comparable to one that fueled the Crusades.
And I agree with your stated differences. Western Civilisation has indeed changed since medieval times. Nnot necessarily for the better, either, as it cannot any longer be called "Christendom". I also agree that this present darkness is adequately covered on other threads. I would suggest, however, that study of the medieval Crusades might reasonably be approached from the "lessons (to be) learned" point of view. What was done right then? What was done wrong then? These questions can be moral, strategic, tactical, other, or some combination. In so far as we are still fighting the same enemy, nearly a millenium later, such lessons could be highly instructive. However they should, as you requested, be addressed within the context of their time .