It honestly doesn't matter what House Jon Snow represents. He clearly doesn't care, he literally bent the knee to wildlings, the Knight's watch and Targaryen just to gain an ally for the greater threat. If you've been watching closely the Houses don't matter anymore, you had a room of noblemen throw away duty and sworn in a man who to their understanding is a bastard. You saw Stannis create his own banner as a false god, house Lannister tell everyone straight up their (Cersei and Jamie) children are product of incest, you saw Khaleesi liberate slaves and form a team that's a melting pot of all the houses and groups in the show.
Whether Snow bends a knee and to who doesn't matter. You niggas fighting over shit I'm not even sure the characters give a fuck about.
