Sorry, this may not be a top-level response, but I wrote a short paper on this last semester and have at least a certain perspective to share. I can't shed much light on those held by the followers of the Roman Catholic Church, but it's important to note that other variations of Christianity existed in the East -- most notably, the Eastern Orthodox Church. The "Great Schism" occurred just a few decades before the First Crusade; I understand that this schism was mostly a disagreement over minute differences that may not have had very powerful historical implications at the time, despite what its name implies (but which rather set in motion a historical process of divergence). However, the two sides of the Schism were quite different in their approach to the Crusades, and the notion of 'Holy War' in general. Some of the following is pulled directly from my paper:

The Catholic crusade was a brand of holy war that was distinguishable from a conventional war in several aspects; it was a war proclaimed by a religious figurehead, called in the defense of the faith, and offered martyrdom and remission of sins to its combatants. The Byzantine 'holy war', by comparison, featured none of these characteristics. Even the proclamation of a “holy war” was the duty of the Emperor (who admittedly also happened to be the effective head of the church, although I don't believe this was official). For the most part, it appears that the Byzantine “holy war” was effectively indistinguishable from any other form of war at all. The infusion of faith into combat was a noteworthy feature of Byzantine warfare; preceding battle with prayers, communion, and attempting to invoke divine favor. However, this was evidently standard procedure of the Byzantine army at large, irrespective of the enemy's religion.^[1]. Religious connotations were heightened in preparation for battle against religious enemies, but the same procedures were invoked even against enemies of the Christian persuasion. As further evidence to the the point, in the commemoration of imperial victories upon triptychs, presumably no indication of the enemy's religion is given. They are only referred to as “the hostile ones” or other “powers”^[2].

The Byzantines in fact appeared to exhibit a sense of hostility towards the Western concept of the 'holy war'. In the early Christian Church, St. Basil of Caesarea wrote that killing in warfare, no matter the imposition of necessity, was still a tragedy that demanded penance from the soldiers responsible for killing – ideally for three years. With this in mind, the involvement of Catholic clergy in the bloodshed of the crusade was especially troublesome to Orthodox philosophers. Evidently when the emperor Nikepheros Phokas requested that the Synod of Constantinople grant the Byzantine armies martyrdom if they fell in the defense of the faith, in an effort to combat the powerful ideology of the Muslim jihad and raise willing recruits, the synod flatly rejected his request. Despite not requiring the penance that St. Basil suggested, it seems that his philosophy underscores their perceptions.^[3] As an example of differences of opinion, later on during the First Crusade, tensions surfaced over exchanges of prisoners between the Byzantines and Seljuks – Western crusaders who witnessed the good treatment of Muslim prisoners remarked that such was a betrayal to the crusading spirit^[4]. Further, the lack of enthusiasm that the Byzantines displayed for the holy war against the “Ishmaelites” stained Byzantium's reputation, as it called into question their loyalty and participation in the Christian community. The Byzantines had a long history of direct contact with people of other faiths, often under the direct sway of their Empire (such as Nestorians and Miaphysite Christians), and often made use of Pagan, Catholic, and Muslim reinforcements in their battles.^[5]

Thus, to my understanding, the First Crusade was really more like a war fought in parallel to the Orthodox Byzantine reconquest of Anatolia and the Levant. The alliance between the two churches was always contentious at best, and at times spilled into open violence. I believe that expelling the Turks from Anatolia was always more of an imperial imperative than anything else. The Pope was very much interested in expanding and projecting Catholic power; as the anxieties of Alexios I in attempting to reaffirm Byzantine stake in the region demonstrates (re-affirming the feudal oaths of the Crusaders to try and maintain suzerainty over expansion). It's clear that Alexios was more interested in the expansion of Byzantine than "Christian" power -- his original hopes were for Western troops and mercenaries that could be integrated into Byzantine command. Instead what he got were innumerable and untrustworthy hosts of Latins that sought to underscore the power of the Eastern Church and Empire in general. Anyway, I apologize in advance if any of this is off or relies on out-dated scholarship!

[1] Oikonomides, Peace and War in Byzantium, pg. 66
[2] Oikonomides, Peace and War in Byzantium, pg. 73
[3] Wright, On the Margins of Christendom: The Impact of the Crusades on Byzantium, pg. 61
[4] Lilie, Byzantium and the Crusader States, pg. 6
[5] Anna Komnena, The Alexiad, pg. 14. Komnena describes the civil war against the
Byzantine general Nikephoros Bryennius the Elder, where the Emperor Michael VII Doukas
summoned Turkish reinforcements as allies to his cause. I believe this happens a few times
following the Battle of Manzikert, but preceding the death of Sultan Malik-Shah I -- such
as during the invasions of Robert Guiscard against Nikephoros III Botaneiates (who was 
himself placed on the throne with the aid of Turkish troops). In fact, Komnena even notes
the presence of Manichaean soldiers in the Byzantine army during this campaign (pg. 103).

"The Crusades" is a relatively recent title for a variety of different wars lead by different people over hundreds of years who often had different reasons and theological justifications for their actions. Eastern Orthodox, Oriental Orthodox and other Non-Catholics would have rejected different theological points that justified Crusading and could condemn the entire idea. Roman Catholics of the time tended to criticize individuals and their actions as unchristian, and these are some very useful primary sources.

Roman Catholic judgement against Crusaders goes as far as Pope Innocent III excommunicating the participants in the 4th Crusade (who brutally sacked Constantinople and other East Orthodox cities).

Yes, Jan Hus and John Wycliffe both spoke out against crusades that took place during their time.

In 1411, John XXIII, (who was considered a legitimate pope at the time but would later be declared an antipope) called for a Crusade against the King of Naples, who was protecting one of his rival papal claimants. Jan Hus delivered an address called Quaestio magistri Johannis Hus de indulgentiis, in which he spoke out against indulgences and argued against the idea that the Pope had the right to order Christians to take up the sword in the name of the Church. Hus said that the proper course of action would be for the Pope to pray for his enemies.

Hus based these ideas ideas on earlier works by John Wycliffe, On the Church and De absolutione a pena et culpa, in which Wycliffe spoke out against the Despenser's Crusade, using pretty much the same argument about the Pope not having the authority to order Christians to fight for him.

It's funny that your interpretation of the Normans is one as a hard core, "right wing " style when nothing could be further from the truth. If you look at the history of the Normans in Sicily and Southern Italy, you will see 2 things: 1 - a large degree of mutual hostility between themselves and the papacy, and 2 - a religious and culturally cosmopolitan society. The Siculu-Normans were Catholics that ruled over a mixed population of Catholics, Greek Orthodox, and Muslims, and allowed them to practice their religions, maintain their places of worship etc. Only when the House of Hauteville was overthrown was there large scale persecution and expulsions.

In terms of crusading zeal, even the Byzantines viewed Norman participation with a particularly cynical eye. They, perhaps rightfully so, understood their crusading zeal as an opportunity to expand the Norman conquests of the 11th and 12th centuries. Only 10 years before Bohemund arrived in Constantinople as part of the 1st Crusade, he had been with his father Roger Guiscard's army, invading Byzantine territory, dealing Emperor Alexios Comnenos a devastating blow at Dyracchium. Only political strategy, Fabian tactics, and an opportune breakout of plague in the Norman camp had kept the Normans from marching on Constantinople and putting a pretender on the throne.

The most compelling evidence against the idea of the Normans as some religious nut cases is their behavior during the 1st Crusade. Bohemund had sworn an oath to Alexios to return any lost territory they recovered for the Greek emperor as part of an agreement allowing the crusaders to cross the Bellspont into Asia Minor. As soon as Bohemund was sufficiently far from Constantinople, he reneged on this agreement. He took Antioch, and created a Norman principality there. So uninterested was he in the crusade that he didn't even go to Jerusalem - he spent the time consolidating his hold on the Syrian coastline and Antiochine hinterland.

So, in conclusion, the Normans were not the avid crusaders one might think. They were ambitious conquorers that gave lip service reverence to Catholic Christianity (one Pope even died in their captivity after they ambushed him and cut his army to pieces, how fervent could they realy have been?!). They were extremely pragmatic about religion, more so than any other participants in the crusades