Islam and Judaism are very theologically similar. There are only a handful of differences: Islam asserts that Muhammad is the last prophet, but Judaism claims that the age of prophets had ended with the Temple's destruction and would not resume until the Messianic Age; Muhammad proclaimed a new set of laws for Muslims, contained in the Quran, which differ in significant ways from the laws contained in the Torah; and Muhammad asserted that Jesus was the Messiah, which Jews categorically rejected.
Arabian Jews rejected Muhammad for these reasons. And it was because of this rejection that Muhammad changed his tone towards Jews - calling them cursed, calling the Torah corrupted, and switching the qiblah from Jerusalem to Mecca.
If Muhammad had not made those claims, but instead styled himself as a Jewish reformer preaching Torah and rejecting Jesus entirely, so that Jews accepted him as a great sage and Rabbi ... what then? How would Medieval history have been different?