Yes. The Christian Scriptures (Old and New Testament) present a God distinct from the Jewish understanding (based primarily on the Pentateuch and the Telmud) and Islamic understanding (based primarily on the Qur'an).

The numerous creeds and confessions of the Christian Church also further solidify the distinctions between Christianity and every other religion, especially the so-called "Abrahamic" ones.

The Scriptures are brimming with trinitarian imagery, language, references, and affirmations (including in the Pentateuch) rejected by Jews and Muslims.

Jews and Muslims also have very little in common with one another doctrinally, by the way, but they share in a rejection of God as trinity and especially of Jesus as one of the three persons of the trinity.

Where misunderstanding becomes idolatry is a really interesting question. It depends on what constitutes the identity of God. If you mean "the ultimate", then you can say that everyone worships the same god, but "same" loses its meaning. On the other hand, if you draw a distinction between the gods worshiped by different sects of Christianity based on our conception of him (for example, whether he is physically present in the eucharist), then you commit the "no true Scotsman" fallacy, which is what you're objecting to here, and it becomes a purity test which no one can pass (no one fully understands the nature of God, and so no one actually has access to him). So there must be some kind of middle ground.

I think of this in terms of identifying your father. What constitutes your father's identity? Is it that he loves you? Or provides for you? Or is genetically your father? What if someone is adopted without knowing it, does that justify calling his adoptive father his true father? You have to define your terms — and it's ok to talk about emotional or genetic or emulative fathers in different contexts. But once you define your terms, those terms dictate who qualifies as your father.

For me, the Trinity and the incarnation are two sine qua nons of the Christian doctrine of God. Faith traditions that explicitly reject those doctrines are explicitly rejecting essential characteristics of God. That doesn't mean their faith isn't related, or derivative, or helpful in some way. But according to Christian doctrine it's not saving faith (Romans 10:9). For human semantic purposes you have to draw the line somewhere. And I think saying "we all worship the same God", while justifiable in some sense, is more misleading than helpful because it's what our postmodern, subjective view of God is amenable to already anyway (and makes the individual into the ultimate arbiter — i.e., God). The world doesn't need platitudes, it needs definition and clarity about who God is — and that Jesus is Lord.