You are incorrect. That is not controversial. In a sermon delivered by Apostle Paul in Athens, he even tells the pagans they may be worshiping the same God but not know it. [0] Paul was probably the least flexible or accommodating of the first Christian teachers.
What is controversial is the details. While Muhammad was inspired by Christian teachings, specifically Nestorianism [1], later Islamic scholars declared that Christian teachings were corrupted [2] thereby nullifying any contradictions between Jewish, Christian and Islamic teachings.
So yes, a Muslim theologian might truthfully say Islam is a superset of Christianity and Judaism, but they are not referring to any known version of Christianity or Judaism.
Christians on the other hand consider themselves a superset of Judaism. For the most part they don't dispute Judaism (as it existed before 0AD) and think of Christianity are an updated/evolved version.
[0] https://en.wikipedia.org/wiki/Areopagus_sermon