"Would you react to this situation differently if we were talking about another religion?"
I've dubbed this question the "Alternate Religion Comparison" (ARC). It's hardly a new idea, but giving it a name makes it more salient and easily communicable to others. The ARC seems to apply in a remarkably wide variety of situations. In fact, I've already used one in an earlier post (see the second to last paragraph). I tend to use Islam as my example because it's a major religion, it has the same roots as Christianity, and it's often viewed negatively by Christians. Here's an example of a situation where the ARC could be useful:
Christian: My friend told me a story about a woman who was suffering from brain cancer. Her family prayed that she would be healed, and she was! Isn't God great?
Skeptic: Well, if the story is true, it's great that she got better. But would you accept that anecdote as evidence for Islam if the same thing happened to a Muslim?
Christian: Well, no...
Skeptic: Then why are you accepting it as evidence for your religion? Isn't that a double standard?
I don't think there's any convincing way the Christian could answer. I suppose they could answer "yes" to the first part of the question, but that's pretty unlikely. I would probably call their bluff with something to the effect of "Really? If a Muslim came to you and told you that story, you would consider Islam more likely?" Ultimately, if they're being honest, I think they'll have to admit that they would shrug off the story as fake or a natural phenomenon. And if that's true, they should do the same with the ones that favor their own religion.