I don't think about a person's racial heritage often. To me, people are people.
This is a demonstration of white privilege. Black and mixed-race people often have to think about race when they are on the receiving end of racism. You (and Danny) are in the fortunate position of not having experienced that.
I think this is the crux of the matter to be honest. As a white person, I had never even considered 'skin coloured' plasters would stick out like a sore thumb on brown and black skin. It had not entered my head as being inherently wrong not to have different 'skin coloured' plasters available. Likewise when I go into Boots and see all the pale shades of foundation, I don't think to myself "but what if I was black?" We simply don't think about it, because we've never had to.
A monkey to me? "Cheeky", "speak to the organ grinder, not the monkey", "a monkey in a suit could do a better job", "more fun than a barrel full of monkeys". Monkeys are synonymous with mischief, silliness, foolishness etc. If you're not a fan of the royal family, or the media 'circus' that parading a new baby entails, you might well unthinkingly post a picture of a monkey in a suit. But probably only if you're white.
Fwiw, I have very little interest in the royals and only recently realised MM is mixed race heritage. Until then I'd have said she looked Spanish, had Mediterranean olive coloured skin. It wouldn't have occurred to me because I too just see people as people and wouldn't think about a person's racial background. It's not necessarily racism, but it's definitely ignorance and white privilege.