In light of Keziah being attacked for her prom dress, let's break down the concept of cultural appropriation.
Cultural appropriation occurs when a "dominant" culture adopts parts of a "minority" culture, like when a white person wears dreads or a kimono (or both). The logic behind cultural appropriation says that it is harmful when dominant cultures take what they like out of minority cultures; some people call it a form of colonization. Cultural appropriation can occur regardless of the surrounding context or the nature of the item being worn as long as you're from a "dominant culture".
This concept is largely America-centric as most examples of cultural appropriation involve white people as the dominant culture. Most people who are concerned about cultural appropriation have no regard for the culture of white Afrikaners (but clothing is the lease of one's concerns during a literal genocide), Slavic people, or traditional European cultures. Ironically, refusal to adopt foreign customs was one of the biggest signs of xenophobia. Though things have changed, I don't think cultural appropriation is as big of an issue as some people make it out to be.
Culture is not a monolithic entity. It's a thing that comes and goes in waves and that people try to preserve through things such as certain lifestyles, foods, and clothing choices. Heck, even the Internet has a culture in which attention is a currency (especially on Steemit), social media is a newspaper, and identity is not limited by human flesh. Personally, I think items of clothing like this should be worn in the contexts they are meant to be worn in. Natives of the "appropriated" culture themselves usually don't care about--and even appreciate--others wearing traditional clothing items like saris or kimonos. It's usually the Americans who disapprove of it.
If you want to avoid any disrespect, research the context of the item you want to wear and decide if it's appropriate for you to wear in that context. In some cultures, that item may be the equivalent of a T shirt, evening gown, or military uniform. Cultural exchange is the natural result of peaceful coexistence, not "colonialism". Don't wrongly credit a culture or person with coming up with something either, like thinking Miley Cyrus invented twerking. All in all, if you use common sense and decency, you should be fine.