The "same God" controversy is still going full steam. I'd like to discuss a popular illustration. According to this illustration, Clark Kent is to Allah aa Superman is to Yahweh/the Trinity. Just as Clark Kent and Superman are coreferential, Allah and Yahweh (or the Trinity) are coreferential. The same individual under different descriptions.
However, the illustration is impotent to prove the point of contention. Let's begin by asking what makes it the case that Clark Kent and Superman are the same individual:
i) At one level, that's simply the case because the narrator says so. Fiction involves truth by stipulation rather than truth by correspondence. Clark Kent and Superman have no real-world counterparts. Reality is not the frame of reference. Fictional characters are whatever the narrator makes them to be. There is no objective basis of comparison, above and beyond the world of the story. In religious matters, by contrast, whether or not religious claims match up with reality is all-important.
ii) In addition, Superman illustrates the principle of dramatic irony. The viewpoint of the audience stands in contrast to the viewpoint of the characters. Within the story, most characters have compartmentalized knowledge of the protagonist. They either know him as Superman or Clark Kent, but not as both. They only see one side of his double life. Part of the humor and dramatic suspense lies in socially awkward scenes in which the protagonist labors to conceal his true identity. How he tries to keep his double life separate.
By contrast, the narrator clues the audience into the fact that Superman and Clark Kent are one and the same person. And this is often less a question of telling than showing the audience his true identity. A movie or TV series shows the audience scenes of the character's double life. Viewers can see for themselves that Clark Kent is Superman and vice versa.
iii) Finally, the Superman mythos is such a fixture of American pop culture convention that most viewers already know his true identity. The director can take that for granted. Every time he does a new episode, he needn't present the backstory of Superman. Rather, that's a given. That's a convention of the genre.
iv) What makes that work is what makes the analogy fail, for the analogy assumes the very point in contention. The analogy can't be use to prove that Muslims and Christians worship (refer to, or believe in) the same God. For the analogy to work, you must first prove their identity independent of the analogy. The comparison can only be brought in after the fact to illustrate their identity. Unless you establish their identity in the first place, the analogy begs the question.
What is crucially missing from the comparison is the required backstory. For instance, when Bram Stocker wrote Dracula, he had to explain the nature of vampires to his readers. That was a novel character. But once the genre becomes established, directors can skip the exposition. The viewer should be able to supply the missing information on his own.
v) In one respect, the analogy can be made to work, but even that has a catch. A religious pluralist could say that just as the same narrator created Clark Kent and Superman, just as the same narrator made both to be the same individual under different guises, the same God inspires different religions, the same God inspires divergent representations of himself.
vi) Of course, there are fundamental problems with that interpretation. To begin with, it relativizes the unique truth claims of Christianity. On this interpretation, the Christian God isn't God in himself, isn't what God is really like. Indeed, there is no frame of reference to say how similar or dissimilar that persona is to God's true identity. Given religious pluralism, God might be a malicious deity who takes fiendish delight in fooling everyone.
vii) But religious pluralism suffers from a catch on its own grounds. The understanding of the pluralist ought to be analogous, not to the transcendent perspective of the audience, but the immanent perspective of characters in the story. A pluralist acts as if he alone enjoys a God's-eye perspective on reality. But the dilemma for religious pluralism is that if it were true, it could never be known to be true. His position is premised on a standpoint which his conclusion denies. For the pluralist is inside the story, not outside the story. At best, religious pluralism can only be an unprovable postulate.
viii) Finally, there's a reverse comparison. Consider stories about identical twins who can pass for each other. Take Alexandre Dumas's The Vicomte of Bragelonne. Rather than having one character under two dissimilar descriptions, you have two characters under almost indistinguishable descriptions.
If two descriptions can be so alike as to be nearly indiscernible, even though they pick out two different individuals, then surely there's no presumption that divergent descriptions pick out the same individual.