The lady involved is a professor of political science. She does not appear to be a Muslim, she is simply was "showing solidarity" toward Muslim women in wearing the headscarf (hijab) and making her now-famous facebook post that includes this: "I stand in religious solidarity with Muslims because they, like me, a Christian, are people of the book. And as Pope Francis stated last week, we worship the same God." (see her full post here)
A lot of people thinking about this right now. Lots of helpful attempts to define and illustrate the the problem. Two thoughts dominate my mind.
The first is to simply re-iterate a powerful "parable" provided by Robert Jenson, itself modelled on another (Jenson states) by Ludwig Wittgenstein: Suppose that in a room containing several persons, I ask one of them to go stand in the corner. Whatever that person does, the rest of us will usually be able to decide whether or not he obeyed me. But now, suppose I draw an arc on the floor in the corner and ask the group whether someone who stood inside the arc would obey my request and they all answer yes. Next I draw a slightly larger concentric arc and repeat the question, and so on. At some point the group will begin to disagree about whether someone who stood in the latest arc but outside the one just previous would have obeyed my request. Then we may be tempted to wonder where "the corner" is and to suppose something ambiguous in my original instruction—when in fact there was nothing at all ambiguous about it. The instruction, "Go preach the gospel," can be perfectly clear and may be decided on even if the several instructors give no agreed, uniform definition of what the gospel "is." (Robert Jenson, On the Problem of Scriptural Authority, p240).
The One God is understood differently between the two faiths. But also, although hopefully to lessening degrees, within each faith the understanding is different. Go the full distance and you finally realise that everyone holds their own unique perception of exactly who the One God actually is (or where the "corner" is). If difference of perception could be measured, it would obviously have to be continuous and not discrete data. Any individual attempting to carve out boundaries (see Carl Medearis http://www.amazon.com/Speaking... rather than trace dynamic trajectories will be imposing some form of imperialistic approach by definition.
So to claim that the attributes are different therefore the God is different is nonsense. If you think that God is love and you are a Christian and the Muslim agrees with you, but your abused doubting-but-still Christian friend still believes in the Christian God but is struggling to sense God's love, how does that work out? The content of LOVE is unique to all of us anyway. I really don't think attributes won't cut it.
Since such strongly voiced opinions are voiced with such strength, you might be forgiven as an outsider to think that since God himself appears silent in this debate, that He might be allowing others to appear ridiculous in their appearing to be his mouthpiece. Ultimately the question should be if there is such a God as the One God, who is more in "corner" than another, would he feel identified by those hailing a different corner? Or would he not notice? That was my second point - God's perspective. Of course, it is theoretically possible that assuming the true existence of One True God, that none of the "monotheistic" faiths have really got close to nailing who he is, perhaps through divine intention. Since perfectly "nailing it" is out of the question, I think this argues for grace and flexibility of that God if he accepts any of us, based on other principles than correct identification.