The problem here is that in order to believe this---Christians must believe in "incarnation/avatar"---that God incarnates into created form. This essentially means making this "created form" into God. Which constitutes idol worship. ----that is, believing that the "created form" is God, or equal to God.
Since God is not "created"---to arbitarily (and falsely) elevate a "created from" to God or equal to God essentially creates "a partner" to God---that is God the "Uncreated" Supreme God and God the created/incarnation/avatar. ---It is the same problem that we would have with Hinduism. The Hindus could argue till the oceans run dry that they are monotheists (though they are not as stubborn as Christians)---it (incarantion/avatar) would never be acceptable as monotheism
I've responded to your comments last, because I see in them the most logic argument among the above as an objection to the concept of the incarnation from an actual Islamic point of view, rather than a humanistic one. But still I have some more questions:
The gist of your argument seems, to me at least, to hinge on the idea that God cannot exist in some sort of created form and still be God. I ask, why not? If God is God, why should he be so limited that there is anything that he cannot do? This is not like asking an illogical nonsense question on the order of "If God can do anything, can God make a rock so big that he cannot move it." Rather it appears you have begun with an apriori assumption that there are indeed things that are beyond God. And I find it hard to so limit God. Why is it that you do not share this concern over limiting God? And yet, even as I ask, I know that you probably do not see yourself as limiting God. And that is why I return with the simply question: Why not? Why cannot God take on created form if he so desires to do so?
I disagree with you that taking on a created form is to make God himself a created being. He would still remain the uncreated being even as he appeared within creation. He simply is revealing himself to more of our senses, but it doesn't change who he is any more than a woman changing her hair color changes who she is even though she may appear different to us.
Consider that any form of revelation is to make God enter into creation in some way, for even our thoughts and ideas are a product of creation. Though they may not take on physical form, but they do not exist independent of the act of creation. So, even for us to think about Allah in the abstract is to do the very thing which you object to with regard to the process of incarnation. For our ideas about God are not actually God himself, they are our projections of the nature of God. And none of us are able to fully perceive or know God in his completeness. We at best each have our own limited understanding of how he is. So, each of us in a sense worship a different God of our own creation, rather than the one true God who exists completely apart from us. At least in the incarnation God is projecting himself to us, rather than we projecting an image of him in our mind.