I also don’t know where you got the idea that islam teaches that god has a body. It doesn’t; this is why the rambam held it was mutar to pretend to be a Muslim, because they believe in the same G-d as we do, essentially. Christians developed the god body thing, they said that god put himself in a body, i.e. yushke r”l.
Muslims say Mohammed was a prophet, and some groups say that Hashem gave over control of parts of creation to him, which is shituf and problematic( i don’t think this was the case in the time of the rambam)