I think many people are assuming that any objection to this kind of casting (putting black or Asian actors in historical roles which, come on, we KNOW were actually caucasian) comes from "not wanting to see non white people on the screen".
It probably does, in the case of some complainers.
But I think there is a more thoughtful reason for objecting to this: it's basically lying about the past, and in particular it is really really telling lies about race relations in the past.
If you have black or Asian actors just randomly playing regular roles in the script while the white characters drift around smiling happily at said black and Asian characters without comment, and being almost preternaturally color-blind, it's telling really big and obvious lies about what people and society were like centuries ago. We know they wouldn't have been like this. People in the 16th century were incredibly prejudiced, openly bigoted, about pretty much every topic under the sun, including race, by modern standards.
It's basically asking viewers to believe "We are in the 16th century, an age when men beat their wives and flogged their children, when servants were spoken to and treated in a manner we would find utterly shocking today, when people who believed in the wrong ideas or followed the wrong religion were put in the stocks, whipped, imprisoned, hanged or burned, AND YET guess what, these unreconstructed bigots just happen to be beautifully race blind and toooootally don't even, like, NOTICE the race of the person in front of them---to an extent which would be quite striking even in people living in 2020! Well, isn't that special?"
It's jarring, it's at odds with everything else about the period, and we know it's bollocks.
How about creating some new, innovative and interesting historical dramas which feature more non-white period, if black and Asian actors want to do historical drama? I can think of about fifty things like that which would make amazing historical series or films. How about a series on the Chinese immigrants who came to Limehouse, and the British women that many of them married? I'd find that a really fascinating subject. And it would be something that felt real and would not involve telling really silly lies about the past.