I don't think being a lady of colour has anything to do with Megan's unpopularity in certain sectors. If Harry had married a white 'commoner', divorced with maybe a starring role in EastEnders or similar, then the Press would have reacted in a similar way. The Duchess of Cambridge has a 'pedigree' of sorts, albeit not Royal, privately educated and demure, just as 'she should be'. I'm sure she is a strong woman in her own right though, she just gets her way in a different manner.
On the other hand the Duchess of Sussex is a self-opinionated brash diva, divorced with a dubious family background and shaky acting career. Take the colour aspect out of this and the Press would still act the same 'she is not worthy' apparently to be in the British Royal Family, and unfortunately has made few, if any, concessions to her behaviour . Its all about her, Megan wants therfore Megan gets. This attitude has made her unpopular with more conventional people who believe in self-sacrifice and duty. Conversely though, her popularity is rising within the current 'Me! Me!' generation, reflecting the changing attitudes towards personal responsibility and moral obligations.