Cultural appropriation?

Okay, this is a long one, but I'm honestly looking to have some understanding here. I recently watched a TV show called Switched at Birth and in one of the episodes, a white RA puts together a "dress as your favorite music artist" dorm party. He dresses up as Lil' Wayne, wearing baggy clothes, a hat with braids, and a foil "grill." Many on campus get angry because he's "appropriating black culture." (Quoting the show).

My question is, if you're dressing up as a specific person that is another race than your own, are you appropriating that culture?

If so, are little girls appropriating other cultures when dressing up as Disney princesses. Like if a little white girl dresses up like Tiana, is that not ok? Honestly just trying to understand. I feel like if you're dressing up as a specific person, it's not appropriating a culture, but I'm open to explanations of why it is! And if it is, does it go both ways?