You keep asserting this, and it's contrary to the assessment of most historians as well as the testimony of a great many of the participants. Do you have any evidence to back your claim?
While I appreciate your ability to Google you are just going to have to do some reading of some historians on the subject. Most books by historians will tell you exactly what I am relating.
Pope Urban II was doing everything he could to stop the fighting of the Franks and bring reforms to the area. He was doing everything from banning fighting from Friday to Monday and on religious holidays and then added a ton of religious holidays to the calendar during the summer months. He excommunicated the King of France and set his clergy on the area to enforce reforms. Once the Crusades were in motion Urban passed a rule that said that while the Crusades were going on you couldn't wage war with other Christians for fear of excommunication.
When the Orthodox came pleading for help from the invading Muslims, Urban used it to encourage the lords to stop fighting each other. He called for a religious war but the underlying message in all of it was for the Franks to stop fighting among themselves and start fighting the invaders.
I would love to say that when the Crusaders came to the east that they pushed out the invading Muslims and helped the Byzantines but they looted Churches, claimed the land as their own, and claimed leadership. Those aren't things that you want to do when you are trying to earn favor with God.
During the reformation the there was a huge revisionist attempt to make everything the Catholic Church did and had done evil and much of that revisionism still sits in the western psyche today. It is so ingrained that many people believe that places like Antioch and Constantinople were Muslim lands and for no apparent reason the Catholic Church decided to attack them and drive them out of the area. That simply wasn't the case. It was far more akin to Iraq invading Kuwait and the west sending help. The major difference is that when America went into Kuwait they didn't pillage the land and claim it as American territory.
I am Orthodox. I have reason to hate the Crusades, and I do, but humans are humans and while there were certainly religious zealots involved, most humans are motivated by other factors just like today.