One alternative way of looking at things that strikes me is that perhaps the Royals - including even Prince Philip - don't actually HATE Sarah the person but HATE the damage that they perceive her to be doing to the monarchy by her behaviour, including her blatant commerical activity, which, however you look on it, is basically cashing in on her NON-Royal status....
In my very humble opinion, it does not help the situation that Sarah is so often seen at social occasions with her girls, and even holding their hands on occasions! [poor girls - and it is all a bit surprising bearing in mind that when Beatrice and Eugenie were much younger, there was much comment about how she was virtually ignoring her childre, always rushing off and gallivanting off without them].
I think that if Sarah was not seen out with her daughters - or to be more accurate, PHOTOGRAPHED out with her daughters [I am not suggesting for one moment that Sarah gives up going to occasions to which she is 'invited for her own sake' and not just as an appendage to her daughters] and instead tried to live more of her life out of the public eye, things would improve for her:there is so MUCH Sarah could do in order to remain below the radar - not walking with B&E etc etc. not going off on all these expensive holidays where it appears that her presence is in some way being used commercially to boost the profile of that place etc etc. This sounds a bit cruel, but I am thinking how Sarah could perhaps help her image, particularly with the BRF, if she started to live a less high-profile and public existence. And I did laugh at the Channel 6 interview in which Sarah was appearing to comment disaprovingly on how she had a public profile - I cannot think of any other person apart from actresses and possibly Sir Richard Branson who have worked so hard on 'being visible'.
Be a little more discreet now, Sarah, and the BRF might find it easier to accept you.
Just my thoughts,
Alex