I have not invalidated racism in the royal family. Harry was one of the biggest of them all. Prince Phillip, definitely by todays more keenly attuned ears, the queen, William and Kate, Charles and Camilla, not that we know of. Lady Husey is not a member of the RF. she was an employee and sacked. Wearing a brooch depicting an African/moorish prince is an example of unconscious bias. I think they've just never given such artefacts much thought.
Whoever made the remark to Harry about any future children's skin colour, whether joking or not, needs to come forward and say what was said. I don't think it was intentionally hurtful, and Chris rock agrees. However it was crass and insensitive and I would say racist. Harry said it was unconscious bias and Meghan said it was too.
People will disagree but UB is something many people have and just need to be made aware of but is without ill intent.
Racism is clearly ill intentioned.
However apart from very few examples I don't think the family as a whole are racist, just simply not educated in equality.
The Princes trust has helped a million young and disadvantaged, people in the time it's been in operation. It's a great charity set up by Charles in his twenties using his own naval pension. Many of those kids helped were not white, but this is clearly not featuring in the bigger picture.