There is certainly a racial element to the OP, whether or not she meant it to be racist.
Saying that if Benedict Cumberbatch payed MLK there would be 'hell to pay' makes the point that white actors can't play black characters without comment, and that seems to suggest that there is more sensitivity given to black people than to white. This is not the case, of course, as (as was pointed out upthread) there are far more roles for white actors than for black, particularly if people are going to object if roles are not matched to people of the same colour as the original, whether in real life or in the book of the film - black James Bond, anyone?
The linking of the casting of Anne as black with graffiti and damage to statues of slavers, which I assume was what was meant by 'removing anything from British history that they don't agree with' is another racial element of the post. This was something that was said by a number of small C conservatives, as well as by out and out racists when the statue of Edward Colston was removed, and is, IMO disingenuous. As has been said, nobody can change history. What we can change is our attitude to events and people from the past, as our understanding of events evolves in line with modern sensibilities, which is what happened with the slavers. Yes, they could afford to be benefactors to a number of cities, but their money was made on the backs of the people they bought and sold and ill-treated. We need to see both sides of this, and if that means that we do not see the need to honour them with statues, then what is wrong with that? If, in a hundred years the feeling has changed, new ones can always be commissioned. None of it will 'change history'.
I am looking forward to the Ch5 series, but until it has been aired, we can't know why a black actor was cast, never mind whether the series is true to what current historians believe to be what really happened. Even that is highly debatable, as all that we can go on is what was written down and has survived for hundreds of years. Where Anne is concerned, the only portraits of her that survive were painted after her death, as Henry destroyed all images of her after her execution, and other than her death speech, there is very little that we know to be in her own words, so her image has always depended on what (largely male) historians have written about her. It would have been a brave man in the Tudor court who would have recorded anything good about her, and a significant number of rumours about her were started by Nicolas Sander, who was a Catholic supporter of Bloody Mary - a motive for discrediting the woman whom he blamed for the schism between the Church of England and Rome.
Subsequent historians have built on these myths and painted a picture of Anne as, variously, a witch, an adulteress, a schemer and a generally Bad Lot. If modern historians are trying to get a fuller picture, or to see her through more feminist eyes, then why not? Surely it is better to put all the information together as it is gathered, and not to insist that what used to be 'known' is all we need to know.
Sorry for the long post, but as you may have gathered, Anne is a particular interest of mine?