From a theological point of view, it is not within our purview to determine who is a “real Christian” or a “real Muslim,” nor do we have any interest in doing so. This is reserved for the adherents of Christianity and Islam.
But being, or not being, a “real Christian” or a “real Muslim” is pervasively used today as a political statement. This is within our purview to comment on, and this comment reduces to one word: hypocrisy. Supposedly, it is politically incorrect to deal in the question of who is a “real Muslim,” but politically correctto label someone a “real Christian” or “not Christian.” Heaven forfend that a terrorist who himself kills in the name of Islam — not only a religious but a political act too — is labeled a “real Muslim,” but Pope Francis has no trouble labeling a politician as “not Christian.”