It is racism but it is also sexism. As an earlier poster said , every woman who has joined the royal family recently from outside the aristocracy has had this in some form ( Diana, Sarah Ferguson, Kate and now Megan).
Meghan is independent and less likely to want to do what Kate has done ( shut up and put up) so she will be even more harshly punished for this
Harry knows this as he was born into it but he is male, born into the family and has a lot of built in goodwill because of his mother's death so he has never experienced what his wife is . Becaue he loves her is trying to help but his lack of experience with this, means he doesn't know how to. I think he genuinely thinks all he has to do is appeal to people to stop and they will . All he is achieving is making it sound like they are complaining and it is making him more unpopular too and subject to claims that he is ' under the thumb' - 
Meghan is being punished for being female and not aristocracy, she is being doubly punished for being older, independent and having some opinions. Being black adds another layer of vitrol from the racists . That means she is being punished three times as much not just twice.
I think both of them are really worried what this will mean for their child as he grows up and are trying to get out of this circus somehow. Good on them