A friend writes in:
What Quinn did is akin, in Judaism, to inappropriate treatment of the Torah during worship. There are specific occasions on which the Torah is read, and specific procedures that are followed in the course of reading from it; it is not done flippantly, or without the observance of protocol, or just because it would be cool to try it out. Can one imagine her behaving in such a manner with the Koran? Doubtful.
Another friend directs me to this nice treatment of “closed communion.”