First of all, it is important to acknowledge that even among Asians, opinions about the whitewashing are divided among two camps. On one hand, we have the usual liberal-minded, progressive community of people expressing outrage about the whitewashing; on the other hand, Japanese fans of the original manga that the film is based on are surprised at the outraged it generated, according to an article on The Hollywood Reporter written by Jasin Boland. It is easy to understand why people were outraged about the whitewashing, because it undermines representation of Asian people in mass media, setting back the progress America has made towards increasing diversity representation in popular media. However, members from the other camp like Sam Yoshiba, director of the international business division at Kodansha's Tokyo headquarters, says, "we never imagined it would be a Japanese actress in the first place." In fact, he focuses on the fact that "This is a chance for a Japanese property to be seen around the world." Other fans argue that in a Hollywood movie, it makes sense to cast a Hollywood actress as the lead; in fact, many Japanese remakes of Hollywood movies have used entire Japanese casts, referencing Akira Kurosawa's Shakespearean adaptations.
The more we think of it, the more it becomes clear that these two camps are really focusing on two different issues. People in the liberal community in the U.S. are mainly interested in the issue of minority representation in media; Japanese manga fans and industry members are more concerned with the business decisions made in making a movie. Minority representation in media is a much bigger deal in America than in Japan because of America's national identity as a place that embraces diversity; Japan is a much less racially and ethnically diverse country and lacks the historical context that America has. This discrepancy thus creates the conundrum of whether it is wrong to appropriate a culture when the culture itself seems to welcome it.
Perhaps we can resort to the philosophical explanation that right and wrong are subjective, depending on what context one looks at the issue in. However, it is worth noting that the American, liberal side of the argument seems to dictate the discourse on the issue, especially when the Japanese side does not care as much. If the Japanese are an important stakeholder in this discourse but we leave them out, what does that say about us?
Asian-American Actresses Discuss 'Ghost in the Shell,' Oscars Controversies: http://www.hollywoodreporter.com/news/asian-american-actresses-discuss-ghost-885890
Scarlett Johansson in 'Ghost in the Shell': Japanese Industry, Fans Surprised by "Whitewashing" Outrage: http://www.hollywoodreporter.com/news/scarlett-johansson-ghost-shell-japanese-885462