The public in general is a group that it's hard to measure the opinion of when talking about the Middle Ages. They didn't produce much if any written works so it can be very difficult to judge their opinion. There is then the extra complication that opinions of the Crusaders changed over time.

Specifically on their Christianity, Muslims would not be unfamiliar with members of the Christian faith. Armenians still lived in the middle east and Byzantium was always nearby (Muslim sources referred to Byzantines as Rum meaning Romans). The actual distinctions between the different types of Christianity don't really show up in Muslim chronicles from around the Crusades. They thought Christians were polytheists for example (whether this was the result of their worshiping of the Trinity, their veneration of saints or something else entirely is not clear). Muslim chroniclers did lump all European Christians into the general group of the Franj (or Franks) regardless of whether they were French, German, English, etc...

On the First Crusade it seems as far as we can tell that the average Muslim didn't much care about the Crusaders. They weren't fond of them but the power structure of the Middle East was extremely fractured at that time and people seemed to view the Crusaders are just another faction in the ongoing battle for control of Syria. There were already multiple Muslim groups fighting each other why not add in some more Christians.

Around the time of the Second Crusade appears to be when opinion went against the Crusaders. There had always been some clerics preaching Jihad against the Crusaders but their popularity seemed to grow around this time and the general Zangi certainly made use of anti-Crusader sentiments to help him take Edessa from them. From there his son Nur al-Din and later Saladin used Jihadist rhetoric extensively in their wars against the Crusaders but it's not really clear how much they, or their followers, really believed it. In Saladin's case he spent far more time fighting Muslims than he ever did Christians.

Thomas Asbridge's The Crusades is a good general history of them, although primarily from a Christian perspective. Amin Maalouf offers a good counter point with The Crusades Through Arab Eyes. If you want to go direct to the primary source I've always liked Ibn al-Athir for an example of Muslim opinions around the Third Crusade.