An age-old question which is coming up today is do Muslims and Jews worship the same God? Here are my thoughts:
To worship the same God is to acknowledge that Jesus is the Son of God. One must therefore deduce that Jesus's Father is God the first part of the Trinity and that by necessity, Christ (the second part of the Trinity) rose again through the power of the Holy Spirit (the third part of the Trinity). They do not believe in the Trinity, but they have similarities in faith-but not enough to say that they worship the one and same God.
As I see it, the similarities in faith are no different to the similarities and basis of Judaism and Christianity. We have the same Father as Jews, but they do not believe that Jesus is the Son of God. Similarities in the three faiths, but without accepting the divinity of Jesus, that one God Who they all worship is not the same to each of them...
Without accepting Jesus as the Son of God, there is no sameness in the gods who they worship. Jesus is the uniting factor. Without Him as God, you have no agreement.