What hat do you wear to a winter wedding? How do you address a letter to an older cousin whom you've never met? Which spoon do you use for the jellied meats course of your lunch? These may not be the exact same questions that plague you today, but that doesn't mean tradition and customs have flown out the window completely. It's just that in the Daisy Miller set, they're going a bit stronger than you're probably used to. And that puts you in good company with Daisy, who's like "what's the big deal?" about practically everything the more traditional characters (Mrs. Costello and Mrs. Walker) hold dear.
It's kind of ironic. They're all in a place that Americans associate with oldness and tradition: Europe (and more especially Rome), but the traditions they honor are their own, mostly made-up traditions. Oh, Americans.
Winterbourne must follow the traditions and customs represented by his aunt because, without them, he has no identity.
Daisy highlights the hypocrisy of all these silly rules by breaking them and forcing others to spell them out for her.