The word 'Honorary' is missing from the OP and it has a relevance to this award.
Of course the problem for some may not particularly be with the award itself but with the dislike of the person the 'Honorary Membership' has been given to for whatever reason but I would suggest in this instance for many people because Kate Middleton is simply a member of the Royal Family.
The Honorary Membership is not necessarily given for the professionalism of the pictures she has taken but as an ambassador for the wider picture (no pun intended) of promoting photography in general, which is the purpose of the Society, at least that is my perception others may well disagree.
About The RPS
The Royal Photographic Society exists to promote photography and image-making and to support photographers in realising their potential, 'irrespective of their level of knowledge', equipment or skills. It has an international membership. The Society also acts as a public advocate for photography and photographers.
The Royal Photographic Society is an educational charity promoting both the art and science of photography and aims to help individuals realise their potential as photographers. It is a membership organisation but, as a charity, undertakes a significant number of activities for the public benefit.
Membership is open to all, irrespective of experience or knowledge. No qualifications are required to join, simply a passion and love for photography or images, its technologies or applications.
Actually I find it rather weird when I read about Honorary Doctorates/Degrees given to people such as Gok Wan, Alex Ferguson, Ryan Giggs or Orlando Bloom. It doesn't bother me though.
Therefore I see no issue at all with Kate Middleton receiving an 'Honorary ' Membership to the Royal Photographic Society to be honest. I do however see a case for the old 'inverted snobbery' to raise it's ugly head or the need to show despise of all things connected to the Royal Family but each to their own I guess.