I would like first and foremost to make crystal clear that I am not racist, do not condone it, find it acceptable, permissible, OK, alright, in any person, be they royal or common, rich or poor, old or young.
As TheTruth pointed out, nowadays there are indeed an increasing number of inter-racial relationships, both on TV and cinema. Thank God! I believe "The Bodyguard", from 1992, is generally accepted as the real breakthrough. However, that was a "mere" sixteen years ago, not even a whole generation.
It is only in the last generation or so that those kind of boundaries have begun to be torn down. Much ground has already been conquered but there is still a long way to go, no doubt.
I did not mean to say or imply that every middle class American or Brit is a white supremacist or something. I know that it is not the case. However, UNFORTUNATELY, there are still large percentages of the population who hold to sayings scuh as "each to their own" and are against interracial marriages, even if they are not racist per se and are quite happy to live alongside people of other races and religion.
Royal families are built on tradition, custom, convention. So (generalising) they tend to be a bit behind the rest of the population when it comes to embracing changes in mindset, morals, etc.
I personally find it laughable to seriously think that a British royals such as Prince William and Harry would ever marry a non-Caucasian. I wish they would! It would be great. But I just can't see it happening. It is already a huge stretch for the royal family to in recent years begin accepting marriages with "commoners", which in reality tend to be marriages between royalty and aristocracy. In the last few years we have finally begun to see some marriages between royalty and working class, but very rare and few and far in between, and even then the "working class" are considerably better off financially than the rest of the population. Considering the inherent superiority of the British people, especially the upper class, and even more so of the BRF, I have no doubt that (unfortunately) most royals would see such a marriage as wrong, degrading, beneath them, or at best, misguided.
There is also another issue, namely the British monarch's status as Head of the Church of England. Although it is permissible to marry anyone who isn't a Catholic, I don't believe that there has ever been any non-Christian Protestant consort in the last 500 years. So again, I really can't see the heir to the headship of the Anglican Church marrying outside it, for fear of discrediting themselves. At most, I think marriage to other Protestant strains (Lutherna, Calvinist, etc) might be acceptable, although I imagine there would be some pressure on the lady to convert, at least outwardly, to Anglicanism, to safeguard the succession and the future religious beliefs of royal heirs.