I think it's obvious why some Jews would want to deny they have the same god as Muslims, and it's purely political. The non-Zionist Jews like Rabbi Weiss still maintain that Muslims and Jews do have the same god. All I've heard so far is Zionist political jargon as to why they don't have the same god.
Why don't you stop spreading this hateful BS? We all know you hate the Zionists, and Israel, etc. We get it. And from what it looks like, many think you do so based on ignorance. But seriously, this whole Zionist conspiracy idea is getting old and tiresome. Stop pretending to be a martyr already.
As for whether or not the Jews and Muslims worship the same God, I would say yes. However, that has always been my understanding. It's the same God, but worshiped in different ways.
Both trace their heritage back to Abraham, and claim to worship the same God. I don't feel like I'm in a position to argue against that. However, there is no question as to whether or not they worship God differently, or see God differently.
I believe the same goes with Christians. As far back as to at least the 2nd century, there were Christians who rejected the Hebrew God. Marcion stands out to me, as well as some other Gnostics. However, both religions, Christianity and Judaism, trace their heritage back to Abraham, and claim, for the most part, to worship that God. However, their ideas about God are not the same.