My friend's White's won't eat wax worms. One of mine will. With Luigi, the first time I fed him a wax worm, he immediately took it from the tongs, and then he let his mouth open wide, and the waxworm rolled out of his mouth. He kept his mouth open for a while, and then he slowly closed it, and opened it, and closed itt, and opened it. It was definitely a "What the heck did you just feed me?" moment.
So yeah. They can be picky. On the same note, Luigi does not like waxworms as much as Baudrillard.