Medieval Christians, as a group, had a very distorted view of Islam. North of the Mediterranean, most had never seen a Muslim. Epics like the Song of Roland depicted Muslims as essentially pagans, worshipping the Roman gods Jupiter and Apollo, and probably as gigantic monsters as well. There was a (completely false) story that Mohammed had originally been a Christian but had turned to heresy.
But along the Mediterranean there were enough Muslims that mutual understanding was at least slightly better. This did not mean that they were friendly--Muslim pirates were a constant concern for Christian shippers. But the lines were not as sharply drawn.
In Spain, which in the early Middle Ages was a patchwork of Muslim and Christian principalities, the two religions had to get along at some level. Muslim rulers often took Christian princesses as their wives, in the hopes that this would make it easier for them to govern their Christian subjects. The semi-mythic hero El Cid fought at different times both for Christian and for Muslim princes. The Christian conquest of the Spanish peninsula, the Reconquista, proceeded in fits and starts and was not complete until 1492.
When the first Crusade was launched in 1095, of course, it was based on the assumption that the Holy Land, "the land that Christ's feet trod" as it was characterized at the time, was polluted by being ruled by Muslims. Christian knights enthusiastically set out to kill Muslims, believing that the warrior skills which would send them to hell if used against other Christians could in fact save their souls if used against Muslims.
But once the Christian Kingdom of Jerusalem was founded in 1100, the conquerors had to settle down and live with a predominantly Muslim population. Many, not surprisingly, adopted much of the local culture, including the food and clothing, if not the religion. Some took Muslim girls as concubines, even wives. The motif of a Muslim woman being converted to Christianity and marrying a knight was common in the epics back home in the west, even if in practice not much conversion may have taken place. Those newly arrived from Europe were often shocked to see this "going native."
Some western theologians were genuinely interested in learning more about Islam, the real religion, not the worshippers-of-Apollo version. Peter the Venerable, abbot of Cluny in the middle of the twelfth century (and thus someone with unquestionable Christian credentials), commissioned a translation of the whole Koran from Arabic into Latin. He took as his starting assumption that it was completely wrong, but he thought the best way to refute its "errors" would be through reason and argumentation, and it would be much easier to argue against it if one knew what it actually said.
Peter is a good example of the twelfth century's happy belief that one could persuade through reason, that a good, logical argument would win the day. In the twenty-first century we've abandoned this. (And Peter didn't win any converts himself that way.)
Incidentally, because Christians, Muslims, and Jews all worship the same God and all trace their roots back to the patriarch Abraham, they are "infidels" to each other, not heretics.
© C. Dale Brittain 2016