A big feature of God for Christians is that He exists as the Trinity. Jews and Muslims do not think of God like this, so we have some difference there. As a Christian, I would say that Jews mostly worship the same God, but the difference of opinion on whether Jesus is God means that each side looks at the other’s God as untrue. I’ve heard a lot of Muslims say that the Christian idea of God is polytheistic, and the way that both religions think of God besides that differ in some key ways.
It is part of Islamic doctrine that Jews, Muslims, and Christians are all “people of the book” who worship the same God. Obviously Jews and Muslims would disagree with the Christian tributary view of God, but in Islamic doctrine at least what would be called “the father” is the same God (Judaism obviously predates Christianity so there isn’t as universal of an interpretation by the religion)
Someone else’s view of God being false doesn’t mean they’re not worshipping the same God, it just means they’re misunderstood the reality of God, just like if someone doesn’t really get you when talking to you they’re still talking to you, even if they have misconceptions about you
That’s a good point. Still, a big part of the Christian God includes Jesus in the mix. From the Christian perspective, if Jesus is not included, then there cannot be God in entirety, which mixes in falsehood with the god that is being worshipped. I would say that the analogy is more like forgetting to add someone to a call or conversation. I’m curious to know what you think about whether or not the same God is being worshipped in the analogy, or if you think that the analogy is good.