I think it's absolutely daft. To begin with, imitation is the sincerest form of flattery - isn't it? Then, nobody thinks twice about people from other cultures, who have come to live here, wearing the same clothes we do. Should someone who originated in another (warmer) part of the the world not be able to wear a winter coat or a raincoat lest they be thought to be culturally appropriating our national dress? It works both ways.
Nobody "owns" style. Everything goes into the melting pot in the same way that our homes have influences from France, Scandinavia, the far East and Africa.