I’m afraid I’ll have to take the side of the whiners in this one. IMO, historical characters should be played by someone who looks as much like them as possible. Thus, Mulan should be played by an Asian actress, Martin Luther King should be played by a black actor, and Hamilton should be played by a white actor. To do otherwise is to degrade historical accuracy.
Fictional characters, on the other hand, should be played by whoever — unless a specific race or gender is specifically called for.
I agree with your points