I am shocked at some of the comments made by muslims about their religion in an effort to “assimilate” others to their way of thinking. At our local high school, one muslim student told his classmates he and his family are “muslim christians” and offerred to teach them about his faith. Fortunately, the teacher in this instance used it as a teaching tool, and after questioning the kid about his belief in Jesus Christ, was able to point out to the muslim student and the class that you could not be both a muslim and a Christian.
But, even in the early days of Christianity, it was common for the monks to tell a people or a tribe who had never heard of Jesus, that they could retain their old customs and just add Christianity. Then slowly over time, the old customs would fade away and Christianity would supplant them. Their Gods and rites would turn into Christian Saints and customs. The former fertility Goddess Ester, becomes the holiday Easter. Fertility celebrations becomes hiding eggs and rabbits on the day of the cruxifiction. And on and on.
BTW, there are a lot of Arab Christians, but I have never heard the term Muslim Christian before. And the teacher is correct. Mohammed was very, very, very much anti-Jewish and anti-Christian. The Koran clearly states that Christians and Jews must be converted, killed, or subjugated. This is no interpretation, it is stated clearly word for word in the Koran.
A Muslim practicing Christianity without conversion and commitment, would be defacing/disrespecting both religions. You have to be one or the other. You cannot be two opposite things at the same time.