I have heard it was just the Pope calling for war against other religions rather than Christians fighting among themselves. I have also heard it was a reaction, which is right?
¿Por qué no los dos?
Seriously, I think you're slipping into a false dichotomy. Historians tend not to think of past events in terms of one:one causal relationships, and if you think about it, life doesn't really work that way. The rhetoric used to justify or rationalize the capture of Jerusalem appeals to the knights of Christendom to put aside their 'unjust wars' with one another and to go to the defense of their brothers and sisters in the East under threat of the foreign occupation and abuse. Pope Urban II's speech at Clermont was prompted by an envoy from the Byzantine Emperor Alexios I Komemnos earlier that spring at Piacenza, calling for aid against the Seljuk Turks, who had been looming ominously over the old empire ever since the disaster at Manzikert in 1071 and the subsequent loss of the Anatolian heartland to the invaders.
Our accounts of the speech at Clermont, written after the fact, are of course problematic, as they have the conquest of Jerusalem in hindsight and vary among themselves in content and focus (though there are some important similarities). While it may be difficult --or downright impossible-- to know what exactly was going on inside 'ol Urban's head, it is likely he was operating within established understandings of sacred violence and holy pilgrimage. In other words, among ecclesiastic intellectual circles, the wars fought between lay aristocrats for land, wealth, and power were viewed as disruptive and detrimental to the Christian community. Instead, If one is to engage in violent pursuits, it ought to be done in defense of that community. The reactions to the events of 1095-1099 certainly seem to fall along these lines. I have recently written a post about how the First Crusade was understood as a defense of Christians and Christendom, if you are interested in more information.
As far as the claims that the Crusades were a reaction to the previous five hundred years of 'Islamic Jihad'-- well personally I find the claims a bit ludicrous. They tend to paint broad-strokes across history, missing the nuance and complexity of medieval history in North Africa and the Levant. There's certainly no reason to assume that Urban II had five centuries worth of grievances in mind at Clermont, nor was Islam a monolithic hive-mind, slowly and purposely devouring Christian lands in a coordinated manner. But for more information (and because it's late here), you may want to try your hand at some of these previous answers on the subject. It's a fairly popular topic:
You might also want to check out the FAQ section Motivations for the Crusades, in particular the post: