"The biggest issue with cultural appropriation is that it belittles the origin culture, in a way that trivializes an entire way of life, turning it into an accessory. If you are a sensitive and respectful individual, the only time it is OK, is with permission or authorization by the origin culture."
From a set a questions and answers about "cultural appropriation," provided on the occasion of Katy Perry's TV-awards-show performance cartoonishly mixing elements of Japanese and Chinese culture.
So — assuming those involved are sensitive and respectful individuals — who must get permission/authorization from what origin culture when the trope is Ninja Pirate Zombie Robot or Samurai Cowboy?
Consider the possibility that the "origin culture" is the United States. Because the name of the culture is pop.
Another part of United States culture is free speech, and no, rest of the world, you don't have to ask our permission or authorization — and you don't even have to be a sensitive and respectful individual — to appropriate our culture, the culture called pop.