0% beer at 18

Hello guys, I recently moved from Greece to the US for university and have been craving having some beer with steak or with some peanuts, something that wasn’t illegal nor frowned upon to do at 18 in Greece. I know in the US I am not allowed to drink until I’m 21, which I don’t really mind as care as I don’t wanna get drunk while having uni to focus on, but what I found surprising was that when I went to a supermarket to buy 0% beer I was told I needed an ID. Is it illegal even though it doesn’t have alcohol, and if I were to end up somehow having some in my dorm and getting caught could it theoretically be a problem (I imagine people wouldn’t really care but I’m unsure). Thanks!