Christians worship the God in Trinity. Jews and Muslims worship ONE God. So would you agree that Jews and Christians don't worship the same God?
It's all about worshipping make-believe fictional deities anyway. However, I don't believe they are all the same 'character'. Even between the OT and NT the nature of the 'God character' of both changes radically.
Mormons have a 'Jesus' in their stuff, but he's not the same character as he is in the NT. These books are not history or non-fiction.
Are you suggesting that because I profess belief in the Trinity that I worship more than one God?
That's a little trickier. As another poster pointed out, Islam is a false construct all the way through. It includes elements of Judaism and Christianity, but not as Jews and Christians understand them. Where there is an account in the Koran that differs from the Hebrew scriptures, Muslims will say that the Hebrew scriptures are a corruption. Where the New Testament teaches, for example, the deity of Jesus Christ, the Koran will tell its readers not to believe that. If I recall correctly, the Koran (or at least Muslim teaching) identifies Miriam the sister of Moses with Mary the mother of Jesus. So not only was Mary a virgin, but she was reeealy old, too!
I wouldn't have any problem with Islam as a creed if it hadn't included false teachings about Jesus Christ. The false teachings are part and parcel of Islam. If Islam did not have that element, I would consider it just another religion.
But back to your question. (And, by the way, Christians worship ONE God, too.) Christians regard the coming of Christ as the fulfillment of promises God made through his covenants with Israel, and extending his new covenant to the world. I know there is some disagreement about whether the new covenant canceled out the old. I would say it has not. And although Jews do deny that Jesus is the Son of God, and do deny the Trinity, if God's covenant is still in force, they would worship the same God but not in the same way, and without the same understanding. And I accept that as God's own business.
Jesus teachings about himself often have to do with his own uniqueness. As a Christian, I am bound to accept what he teaches. But I am also bound to respect Jews. "Salvation is from the Jews," Jesus himself points out.