For instance, say a book is titled "Genesis and Its Interpretations". Is it correct to capitalize "its" in the title?
Technically it should be, since it's officially a pronoun. As far as elegance goes, it probably shouldn't be used in a title at all. Makes the whole thing sound overly bookish and needlessly pompous, even worse, perhaps, than "Genesis and the Interpretations Thereof." Reads almost like "Genesis and How Some Morons Interpret It," which I expect is not quite the effect you're looking for.
Try "Interpretations of Genesis: Quaint vs Traditional," or something.