You see, in Islam, Allah is a monad. Three persons who share a single nature cannot be one God, at least to the Muslim mind.
Only on the most pedantic grounds can it be said that Christians and Muslims worship the same God. Were both religions (along with Judaism) inspired by the dealings of YHWH with a Mesopotamian nomad named Abraham? Yes. But Islam, having originated in the sixth century A.D., is a smidge further removed from those events than are Christianity and Judaism. In fact, Muhammad taught that both of those religions are corrupt, which is why he recorded a new and “perfect” revelation from God: the Qur’an.
We’re not trying to be meanies. Really. We just think the triune God is a non-negotiable. We also believe the canon of Scripture closed with the death of the Apostle John, meaning Muhammad’s revelation misses the deadline by half a millennium.
And since the Apostle Paul told us not to believe anyone, “not even an angel,” who brings a gospel other than the one we received—well, I don’t know how to break this to you, but we tend to think Islam began with a visit from a demon. Given all of this, identifying our God meaningfully with the god of the Quran is not just difficult. It’s impossible.