I think it is difficult for you to imagine a Muslim Christian because it really isn't possible to be one. Someone who follows the teachings of Islam clearly does not give credence to Christian tradition and scripture and certainly denies the divinity of Christ.
I don't claim to be an authority on Buddhism, but there are some posters on this forum who are extremely knowledgeable on the subject. My opinion, however, is that the major Buddhist traditions (I'm most familiar with Theravada and Mahayana) are, in some ways, incompatible with practicing Christianity, in large part due to their perspective on the world, chronology, soul, etc. I have read arguments that Christ is, in fact, the Great Bodhisattva, or something along those lines, but that is not a particularly orthodox understanding. I guess, in a very similar vein as a recent Tai Chi/Yoga thread related to this, my question would be: Is Zen, removed from particularly Buddhist spiritual understandings, still really Buddhism?
I don't doubt that practices such as Zen, Yoga, Tai-Chi, etc have beneficial qualities, but I find it peculiar (please note that I did not write "wrong") that people want to somehow integrate these practices into Orthodox Christianity. I recognize the similarities between Zen and Hesychasm, but Hesychasm is also very different and was developed strictly within the confines of Christianity.