It does rather seem that whiteness is the most important characteristic for some posters.
Whilst I can see that there are some things that would scream as historically inaccurate (Anne wearing a watch, for instance), I wonder how much of what we consider to be 'facts' from history are, in fact, just interpretations that have caught on - often because of one director's view of how to present them?
Even 'facts' about the times we live in are not cast in stone. Ask two people to write an account of Brexit, for instance, and there is a good chance that they will present very different 'facts'. It is the same with history, except that with the distant past such as the Tudor era, there were fewer people who could write, and each time there was a change of dynasty (or in Henry's case, a change of wife) documents and portraits were destroyed, in the manner of a teenager blocking his ex from Facebook and deleting her photos from his timeline?.
There is such a lot that we just don't know, so it is left to dramatists and authors to make a story out of what little information they have to go on.
It is safe to say that Anne was not black, but casting has never really been about getting a replica of the historical character. It is far more about getting someone who fits with the dramatist's interpretation of events.
Just as an actor's hair colour, height, weight etc are not important (to most people) it is surely time that skin colour doesn't matter either? Would anyone say 'I am not watching that programme because it the casting is just to appease redheads. If Damian Lewis said he was going to play the role of a dark haired character, there would be hell to pay'? I doubt it, somehow.