I wouldn't say that's how jokes work. Some things need to be established first. The joke is not, that he is non binary. It's a play with words, "agenda" in this case. Him being genderless is supposed to be the baseline. This is contradicted by him being a Warner brother. So the joke is already falling apart during the setup. If the joke was about him being a chicken, it wouldn't have made sense either, because it was never established before. And can't explained with cartoon logic.

It feels like people are automatically mad at me for criticizing the joke, because the topic is gender politics. I never said he can't be non binary, I don't care, but there was never a basis for this. Or so I thought. As others have pointed out, there apparently was an episode or a comic where this was mentioned.