I think She was saying that even when Charles takes the throne Archie and his sister will not get the titles even though all the other grandchildren will
Which is why she thinks it’s down to race
Only it isn't to do with race. Charles's desire to want to slim down the monarchy once he takes the throne are well known and was being talked about long before Meghan was even on the scene.
As it stands, Harry's children would automatically inherit the title of prince/princess once Charles becomes king. However, Charles wants to slim down I assume because having princes and princesses all over the shop causes confusion and the title brings with it notority and thus protection issues (you can't exactly live a private life if all and sundry have to refer to you as prince xx). The title muddies the water in terms of what we, the public, assume that persons responsibilities to be and their position within the hieracrchy. Its very apparent from all the comments that Joe Public doesn't really understand the technicalities and protocol of titles as the majority of us don't mix in those circles.
Just having William's children as princes and princess makes the heirachal nature of which child is the next direct heir to the throne obvious and fits with the slimming down that Charles wants - only royals with a direct succession get the coverage and perform the royal roll.
However, as Harry is and always will be the son of the king (when that happens) it does seem off that his choice on whether or not his children should adopt the title (as the grandchildren of the then king) has been taken away from him (if that is indeed the case - it may just be that they wanted it now rather than waiting). Whichever way you look at it though, it really does reinforce the heir and the spare narrative in that he will always be the lesser person.
The issue at play here is his relationship with his own father and that duty to Charles is deemed more important than him as a son.