So I did worry a bit about having drinking scenes, since 21 is the official drinking age. Ultimately it felt less true to a Comedic American College Experience (TM) if everyone went "Welp, time to obey the law!"
That said, as Jack said- People sometimes do things they might not otherwise in order to fit in. Part of Anne's motivation early on is trying to "break out" of her small-town, shy - girl shell. To her mind drinking is what these more worldly college students -do-. So if she wants to be like them, or even just unlike herself, she has to join them. She may be a rule follower, but she's also in roman trying desperately to do as the Romans do. And everyone else seems more than happy to throw the rules out the window
So yes, it's in character for Anne, but I can appreciate where some people would have wished for the option to be teetotalers.