Some arguments I've seen in defense of the claim that Muslims and Christians worship the same God remind me of Hinduism. In particular, the Hindu doctrine of avatars, where the many gods of the Hindu pantheon are really just projections of one God, of one otherwise ineffable, unknowable Deity. On that view, Hindu polytheists all worship the same God, even when they worship different gods.
God is like an actor who wears many masks. You don't know what he looks like without the mask. If you caught sight of him without the mask, he'd be faceless.
Indeed, there are character actors like Peter Sellers who admit that their offscreen persona lacks personality. That's why they can disappear into different roles.
The way some folks defend the claim that Muslims and Christians worship the same God is eerily similar to saying Allah, Yahweh, Jesus, and the Trinity are avatars of the same ulterior Deity.