I know I disagree with most, and may be I'm completely wrong, but I think we're being unfair when we accuse Jews and Muslims of worshiping idols or demons rather than the One True God.
The religion of Israel and the religion of the Church, the new Israel today, are not two different religions, but one, the true religion. In the NT we know more of the truth than was revealed in the OT, but when we go to heaven we will know more still, but that doesn't mean we'll have converted to a new religion. We follow the same continuous tradition of our father Abraham, though the full revelation has since been given to us.
Modern day Jews have departed from this tradition. We are the continuation of it, not them. We continue in the worship of the Temple, through its fulfillment in our participation in the heavenly Liturgy of which it was a shadow. Modern day Jews are not the continuation of the Old Covenant. They departed from it and do not have sacrifice any more, so they don't follow the Old Covenant. They are very much analogous to Protestants, both of whom either reject or have lost the Liturgy, and have become "people of the Book".
That said, being in the wrong tradition, and not having the full understanding does not mean worshipping a different God.
Abraham did not know the mystery of the Trinity as fully as we do, yet he surely worshipped the true God. More of the truth was revealed to us when Christ came, and those who rejected that truth were wrong. But they didn't change who they worship. They just believe wrongly about Him. They rejected knowing more of Him. They worship Him ignorantly, but still the worship the One God.
Later Muslims rejected the same things the Jews rejected initially. They understand God wrongly, but I don't believe that that means their prayers and worship is not directed towards Him. If they follow violence and sensuality then perhaps they are following an idol, but if they pursue virtue and goodness, then they have a very wrong knowledge of God, but it is still Him they are seeking.
That doesn't mean they don't need Christ, that they don't need the Church, that they don't need Baptism and the Mysteries. They have rejected the New Covenant, and they do not have the Old. They are estranged from God. Their attempts to worship Him and follow Him are wrong. How He will deal with them I don't know. But when I see a good person seeking God, I can't believe that is an idol or a demon, and not a sliver of the truth of the One God that they are directed towards.