Yes, many Christians are of that conviction. I can see both sides (that the Allah Muslim’s worship is a different God or that the Muslim understanding of the true God is corrupt).
Muhammad certainly was influenced by Jewish and Christian teachings. The bad part is that he picked and chose what elements of revealed truth he wanted to believe and added in stuff of his own.
Even if we granted that Muslim’s worshiped in an imperfect way God the Father, they are still followers of a false prophet and a non-inspired holy book and oral tradition.
This is a non sequitur. Just because
(A) there is one true God who created the world and everything in it and is worthy of worship by all mankind
and (B) there are people who worship what/who they claim is the one true God who created the world and everything in it and is worthy of worship by all mankind
it does not follow that the people in statement B worship the God in statement A.
I could believe that a golf ball is the one true God who created the heavens and the earth and everything in it. I could believe that this almighty golf ball is the same god worshiped by Christians, Jews, Muslims and Zoroastrians. I could bow down to this golf ball and pray to it and pay it homage and devote myself to the golf ball’s precepts and moral teachings as revealed by the great and inspired golf ball prophets. . . .
And yet for all of that . . . I am not worshiping the one true God. I am worshiping a golf ball . . . a deity of my own creation.
The fact is that Scripture tells us there are false gods and false idols that can be worshiped even though they are not gods let alone even living. Moreover, it warns us of the possibility of demonic power portraying itself as an angel of light. Even more troubling is that we see how man has a history of rejecting God and creating a deity according to our own thoughts and opinions.
First and foremost, the Allah that Muslims worship is an idea and a concept. That idea can be false. It can be an idea of God that we (or Muhammad or his later followers) put in everything we think God should be and reject everything that we don’t like about the God revealed in Old and New Testaments.
More sinister is the fact that this idea can be used as a smokescreen that Satan uses to blind and confuse people. It is a counterfeit of the one True God, who can only be perfectly made known to us in the person of Jesus Christ.