I didn't read this thread until today, and wasn't sure if I should address this or not, but decided I was going to. Apologies in advance if it gets lengthy or if anyone reading it disagrees.
First, Hamilton is a show that features a cast of various races and ethnicities, including white, black, Hispanic, and Asian, portraying characters that were largely white in real life. This is an artistic choice to tell the story of the founding of America during the revolution and subsequent years when the government began by using a cast that represents what America looks like now. However, there are not specific casting restrictions or guidelines. The original Aaron Burr on Broadway was played by Leslie Odom Jr., a black man, but the Burr I saw in Chicago was played by an Asian actor (I don't have his name handy, unfortunately). One of the white actors I met afterward is what's referred to as a "swing" actor, meaning he plays multiple roles for different performances, and he told us he played Hamilton the week before we saw the show. That actor was white.
This decision was made by Lin-Manuel Miranda, the show's creator and original Alexander Hamilton, because when reading Ron Chernow's biography of Hamilton, Miranda related very deeply to the story of an immigrant who came to America and made a large impact on the country we know today. As the son of native Puerto Ricans, Miranda grew up in New York and knew many people who reminded him of Hamilton, and he felt compelled to write this musical.
Hamilton is all about America and what it means to be American. You watch it (or listen to the soundtrack) and you get a sense of what America was, is, can be, and should be. It brings history to life for people living today. There is an overwhelming feeling when you watch it that the American dream is alive and well, no matter what race, gender, sexual orientation, religion, or age a person is.
As you pointed out, the Urban Myths show that featured Joseph Fiennes as Michael Jackson was met with a lot of criticism. I understand your point that if one was criticized, the other should have been as well, or neither should have. What's good for the goose and so on. And I don't even necessarily (totally) disagree, but will try to explain why I believe it was met with backlash.
Part of the reason is that the immediate family of the subject was still alive, and could voice their disapproval on the show. If the Jackson family had said "oh, it's ok," and gave the production their blessing, it probably would have moved forward. So that's part of it.
Another part is because Michael suffered from a skin disorder called Vitiligo which caused his skin to lose pigment as he got older (his autopsy confirmed this). So while he definitely looked more like a white person in his later years, this was due to the disorder, so having a white person portray him comes off a bit as mocking an ailment that he had, whether intentional or not.
Finally, I think it also has to do with the people creating it. Right or wrong, the writer and director of this episode were both white guys in addition to Fiennes, so it comes off as people who don't really understand Michael's experience trying to belittle his humanity and also deny representation for a black man on television, whether intentioned or not.
To bring this long poast to a close, I'm not sure what the right answer is. Race is a tricky subject for a lot of people, and they feel very sensitive about it. There are a lot of forms of entertainment that face backlash for issues of race. Some don't come until after the movie's release (the movies Prince of Persia and Exodus: Gods and Kings are two examples), others are met with backlash before the film is made (Scarlett Johansson just ran into this). Sometimes movies are criticized for changing the race of a character (people were very upset with the casting of Michael B. Jordan as the Human Torch in Fant4stic; that movie was bad, but it wasn't cause of him), other times, it's met with approval (Tilda Swinton in Dr. Strange). It can be frustrating for people trying to figure out why some things are acceptable and other things are not, and sometimes the standard for what's acceptable changes. So, I'll leave you guys with a great (funny) song on the subject that comes from another musical I love, Avenue Q, "Everyone's a Little Bit Racist"
