The Muslim god is not our God.
You can have subjective morality, but it doesn’t have the same meaning as objective morality. And it’s not really a valid system of morality.
I don’t see how “the well-being of humanity” is subjective. But a larger point is the implications of what you are saying: that one should believe in God not because it’s true, but because it provides a fixed point for you to base a morality on. As I said, it provided one for the Islamic world too, and they got their idea of God from the Abrahamic tradition, so yes, it’s the same God. You could argue that Mohammed lied about God talking to him and therefore everything they believe about God is wrong, but it is still the same God (who apparently has said nothing to them to correct their mistake. Oddly.)