Mainly interested because recently on Reddit there's been some links to news stories dealing with Christians and Muslims worshiping the same god, and I've seen in the comments occasionally a guy claiming to be a Jewish guy (one specific commentator actually in multiple threads) argue that Christians and Jews don't worship the same god because the divinity of Jesus is incompatible with the Jewish conception of god, but that Islam's view of god was compatible with the Jewish understanding of god.
It made me really curious to know what the Jewish theologians familiar with Islam thought about it. I'm asking about medieval ones because my impression is that that's when the great Jewish theologians lived - and lived in Islamic societies.
The person you are talking with is correct. When Christianity became the most important religion in the Roman Empire, Jewish religious law treated it as an non-monotheistic religion due to the Trinity. Therefore, it was forbidden for Jews to drink wine handled by Christians or to enter a church.
The medieval Jewish commentator who was most interested in discussing relations with other religions (and most influential on the subject) was Moses Maimonides, also known as the Rambam. He states in his commentary on the tractate "Avodah Zara": “Know that this Christian nation, who are making the claim of a messiah, with all their many different sects, are all idol worshippers and all their holidays are forbidden, and we deal with them regarding religious issues as we would pagans.”
In contrast, Islam was treated differently, because it is explicitly monotheistic. Moses Maimonides said in his Letter to Obadia the Proselyte that “These Ishmaelites [Muslims] are not idol worshippers in the least, and [idolatry] has been long since cut off from their mouths and their hearts, and they worship the singular God properly and without any blemish.” Therefore, later commentators stated that it was possible to pray in a mosque if necessary.
On the other hand, since Christians treat the Hebrew Bible as holy, Maimonides authorized teaching the Jewish understanding of it to them but not to Muslims (who think it is incorrect in places). So at least in that sense, he views Christianity as "better" than Islam.
He does see a positive side to the existence of Christianity and Islam:
"All these activities of Jesus the Christian, and the Ishmaelite who came after him, are all for the purpose of paving the way for the true King Messiah, and preparing the entire world to worship God together, as is written (Tzefaniah 3,9): "For then I will convert the nations to a pure language, that they may all call in the name of G-d and serve Him together.""
But overall, he (and other commentators) definitely thought both Christianity and Islam to be wrong in many ways, and vastly inferior to Judaism.