I waited a bit before answering in case someone could provide a better answer, but I think I can handle this one. The question starts with a couple of premises that are not 100% correct. The first is that there was a competition between Islam and Christianity in Western Europe before the Protestant Revolution. There wasn't. Even scholars were barely aware of the details of Islam. And this is tackled by u/WelfOnTheShelf in this answer here -> I'm a Crusader heading towards the Holy Land in 1096. How much do I understand about Islam?

The second is that where contact between Islam and Christianity was common literate people could read the Bible, because it was not in Latin, it was in Greek. Even though Jesus is believed to have spoken Aramaic, the New Testament was written in Greek and the Old Testament had been translated to Greek around the year 130 BC, that version being called the Septuagint.

Greek was used as the trade language of the eastern coast of the Medditeranean Sea ever since Alexander the Great had conquered the region and his generals estabilished kingdoms in which its bureaucracy and its elite used Greek. The practice of using Greek continued during Roman times and in the immediate aftermath of the Arab conquest literate people would still be able to use it