Is it fair to say that Christians worship Jesus and Muslims worship the father of Jesus?

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No. Christians believe that Jesus and God are the same person. All three “people of the book” worship the same thing, the Abrahamic God, but however believe different things about that deity. It’s a matter of semantics as to whether this means the three worship different deities, not anything material.

Islam shares a great deal of scripture with Christianity and Judaism, it’s kind of hard to argue that they all worship different gods when they’re all pulling their knowledge about their god from the same source material.

Even within Christianity there’s arguments over the precise nature of God. The main reason why there’s Orthodox and a Catholic Churches comes down to one of those disagreements. All the arguments derive from Scripture.

But these are incredibly detailed and pointed arguments between people that take this stuff very seriously. It’s a bit like saying string theorists are not physicists simply because they have different ideas about the underlying nature of reality.