Hank "Rusty" Truman asked: In a modern or real-world au, would they identify with any subculture, and if so which one(s)?
I only need to take one look at these kids to know they had a rebelious, punk phase. They're friends with Mai so they at the very least like the goth aesthetic (and they both checked her out many, many, many times), and come on, look at Zuko's hair - that boy had an emo phase.
And obviously, they're into BDSM. Azula is a brat, and Zuko is a brat-tamer. He is usually the Dom (and Azula will sometimes call him "Daddy") but she'll turn the tables on him every now and again because of course she does.