While I can't comment with any authority on the opinion of Nicholas III in particular, I do own a copy of the Alexiad and so I can tell you a bit about that source. While Anna was only a young woman at the time of the Crusade, she did have access to the imperial archives and according to her most of her information comes from "Honest veterans" who went into the church. The first thing she notes is that Alexios was surprised by the size and nature of the expedition, and she failed to mention her Fathers request for aid at the council of Piacenza. She describes the Westerners as barbarian Frankish peoples, but more importantly as dishonest oath-breakers, as Bohemond had taken Antioch for himself in violation of his oath to Alexios (Note that Bohemond being crowned Prince of Antioch seems to have occurred prior to the retreat of the Byzantine army and the subsequent Seljuk siege of the city, which would give Bohemond his justification for breaking his oath). Contributing factors to this attitude were a somewhat justified sense of cultural superiority by the Byzantine populace and the fact that many of the crusaders were the same Normans who had waged war against the empire only a decade earlier, with Bohemond being a son of the late Norman King of Sicily Robert Guisard.

As for the Churches opinion on the Crusaders, while we have little on what each individual member of the chuch thought, there was a considerable cultural confusion among the clergy. The Orthodox thought of war as a necessary component to the defense the state, but not something that was generally looked fondly upon by God (after all, one of the ten commandments is "thou shall not kill"). The Byzantines themselves had fought the yearly Jihads of the Umayyad and Abassid Caliphs, and when the 10th century Emperor Nikephoras Phokas attempted to make the soldiers who died on campaigns against Muslim foes Martyrs in the Orthodox Church, the Patriarch of the time flatly refused on theological grounds. So when large numbers of Christians were promised salvation in fighting a holy war, it was a very alien development to the higher ups of the Church.

If You would like, you can hear more of the specific details about the Normans and the politics of the First Crusade in the First two episodes of my Podcast on the Komnenian Dynasty.

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Sources: The Alexiad by Anna Komnenos

Sowing the Dragon's Teeth: Byzantine Warfare in the Tenth Century by Eric McGeer.