You point seems to be that we make a "distiction without a difference". That is, that we use two names for the same god.
The difference is more than the name. To confuse the two does not reveal your enlightenment, or tolerance, but you lack of knowledge on the subject.
A little research will show that "Yahweh" and "Allah" describe two different mindsets, lawgivers, and beings. If they describe the same being, he's suffering from multiple personality disorder.
In other words, you are obviously correct in pointing out that God is not a Christian, Jew, Muslim, or Buddhist ... nor is He American or Arab. But while there is only one true God, but there are many imposters.