Are you even reading this? It's not the rest of the costume that is problematic, it's just the coat.
Reality isn't even relevant here. We're not dealing with reality, we're talking about what a fictional character in a fictional setting is wearing. Which is the Hollywood dress uniform of sex workers.
Sexy dresses just mean 'female'. Fur coats on women who aren't standing in the snow mean prostitute. The race of the character is not a factor here.