Perhaps a better question is do we worship the same God as Muslims, Jews, and other Trinitarian Christians?
Before we attempt to determine whether or not they worship the same God as us, we need to determine just exactly what God we worship. Given the many disagreements within Orthodoxy and different opinions and theologies of internet Orthodoxy and to some degree (but not nearly as much) in real-life Orthodoxy, it's not as clearcut as many would like to make it. Do "schismatic" Orthodox and "world" Orthodox worship the same God? Do I worship the same God (when I'm not rebelling against Him) as say Isa or Maria?
Anyhoo, I suppose one could argue that a God in the Abrahamic concept of a Creator is by default the same God since they are all viewed as the Creator. You could define God as the Creator and the Abrahamic religions as merely being details about this Creator. The problem is that many people--especially Protestants--are really afraid to get into the details of just what the Abrahamic God is.
On the other hand, St. John politically incorrectly says in his epistle that:
Whoever denies the Son does not have the Father either...
This, at first glance, would clearly suggest that Jews and Muslims do not worship the same God or have the same God as us since they deny the Son of God. I'd also add that one could argue that when you have incorrect doctrines and ideas about God, then you aren't really worshipping God but are merely worshipping an intellectual
idol of God in your mind. But that begs the question: what is God? How do we define God? When do we draw the line between the definition of God and mere predicates about God? Or does such a thing even exist? Or is the former defined precisely by the latter?
I'm personally very uncertain. And I think that Jews and Muslims are as well. I've met many Muslims who believe that we share the same God, whereas others vehemently believe that we share different Gods, some even go as far as to call us polytheists. So yes, there is some confusion within the Islamic community as well in regards to this question.
The only ones I've seen who seem consistent are Jews who, from what I've gathered, seem to believe that neither Christians nor Muslims worship the same God as them.