I've never considered Meghan's racial heritage, either. I know, from the occasional media articles and MN posts that I've read, that she is mixed race, but it's not something that I would have seen for myself and I've never understood why it was ever something to draw attention to.
All I see when I see Meghan is a beautiful, but rather self-conscious young lady who seems anxious not to put a foot wrong.
Therefore, I picked up the "circus performer" aspect of Danny Baker's "joke", not the racism connections that can be made. I don't think he intended to be racist, though he's right to apologise for offence caused.
I wonder what the Mountbatten-Windsors thought of it.