I knew it was transphobic with the "whatever", it was just meant as a tease. You know, there's a "new" word in Swedish "hen" which is the genus neutral combination of the words "honom" (he) and "henne" (she). Some hate it, some find it very useful. If there were such word in English, this situation would perfect for it (or not as I'm maybe in deep water here ).
But Caitlyn Jenner is officially a woman so you shouldn't use gender-neutral pronoun. Gender-neutral pronouns are meant to be used when somebody doesn't not wish to be referred as a woman/man - not when somebody wants to transition to another gender. So no, situation is not perfect for it (at least not now, when Caitlyn is officially a woman).