Could Prince Harry marry Princess Beatrice as they seem to be well suited?

It is legal in England to marry your cousin, but in this day and age the outcry that would come from the public would be terrible. For a family in the position of the Royal family, this kind of a move would be catastrophic, if it were even allowed by HRH The Queen. And most people don't look at their cousins in that kind of a way anyways. I know I think of my cousins in the same way I think of my siblings. The public and Buckingham Palace would have NO tolerance for that kind of a union whatsoever.