I'm not that comfortable with some of the accusations of whitewashing that have been made recently. There are many recent instances, but the key one I'm interested in is Scarlett Johansson in the upcoming Ghost in the Shell movie.
There are certainly horrific examples of whitewashing from decades ago ranging from blackface to exaggerated Asian (Breakfast at Tiffany's!) or Indian affectations. These can be explained away as cultural gaffes of history, like an older person using an impolitic term. It's not great that they happened, but our embarrassment of them as a culture is a sign that we've grown. Recently though there have been very public discussions on and dissatisfactions with European whites playing characters of other cultures and cisgendered playing trans. I feel that the legitimate issue with whitewashing is when, simply, a crude stereotype or one-note character is presented. The stereotype is lazy and racist (*-ist (side-note: I've noticed the word "racist" used as a catch-all for social over-generalization w/r/t race or nationality or gender, and I kind of like its transformation into a catch-all)) and so is the easiest to spot and critically dismiss. The writer or actor doesn't care enough to understand the othered group, and so presents a thin, shadow of a character. What could be a dynamic secondary or tertiary character becomes filler with a check mark for "different".
However, and this is key, actors should be allowed to act. They perform as characters with advanced skills they haven't personally acquired, or with mental aberrations and manias they do not possess and could never acquire or as people that could never exist. Taking that into account, is nationality or gender so out of the realm? Though I haven't seen it, the show Transparent seems to be, critically, the canonical example of a cisgendered actor playing a transitioning character. With quality writing and performance observation, the specter of minstrel shows dissolves into an illumination into the lives of humans of the world.
Over the past few months, I've been watching pinky violence films from 1960s/70s Japan. They generally deal with female street gangs fighting aggressive male competitors, or corrupt government institutions taking advantage of the poor or female or both. In several (e.g. Sex Hunter, the Rica series), those who have mixed national parentage--"half-breeds"--are treated with focused brutality by the alpha gangs and a strong-willed female thug steps up to protect them. In Sex Hunter, the half-breed Kazuma is played by the Japanese/Italian actor--with visually uncertain heritage--Rikiya Yasuoka. In the Rica trilogy, the lead Japanese/American woman is played by Rika Aoki. I am uncertain whether the actress is herself multiracial. Nationality it seems is very fluid.
Back to Ghost in the Shell, it was pointed out in a comment from a recent Reddit thread that five of the seven other main actors are of distinct, non-Japanese nationalities, and I'm reminded that a main theme of the story is that of fluid gender, individuality, and consciousness. This seems key.