I would imagine they wouldn't care, in fact it might play in your favour. Yes universities are really woke at the moment but a lot also have UOTC and stuff so for many they either won't care, or will think you will fit in at the university if there is a big UOTC there. It'll also show your passionate and determined, all good qualities. As long as you don't say in your personal statement: "I want to join the military to drop bombs and kill people" then your fine. I don't go to university but know friends that do, and from what I have seen they treat them like children, patronising etc. If you do show passion to join the military they might just blow it off either way as a "teenage phase". I Would disagree with them, but either way your fine.