I can only speak for myself but I feel sorry for them because I grew up with a girl who was in a similar situation to them.
Her family was very wealthy and her parents were "pillars of the community" until they weren't. The mum and dad controlled everything about what she and her brother did, it was all about maintaining an image; from the way they dressed to who they were friends with, hobbies they had etc.
When she was late teens/early twenties stuff started coming out about people around the parents and what they were getting up to, mainly that they were crooks and were defrauding people. She and her brother were still forced to attend events by her parents because they controlled the money and they needed their cash for uni. They threatened to cut both of them off if they didn't comply.
To cut a very long story short, her parents were found to be stealing from their church and she and her brother ended up getting tarred with the same brush by some parts of the community.
Both children were absolutely lovely, were thoroughly ashamed of what their parents did and had nothing whatsoever to do with their schemes. Everyone that knew them tried to make it clear that there was no way they were involved but some people wouldn't listen and hounded them. It made both of their lives hell for a long time and the end they both had to leave to get any normal life.
I just see the parallels with what Beatrice and Eugenie are going through, although they're on a much wider stage and much more in the public eye.
I understand why your friend's experience would make you sympathetic towards Beatrice and Eugenie, and I agree that children should not be blamed for the actions of their parents. Nobody chooses the family they are born into, and it must be incredibly difficult to have a parent's mistakes follow you around.
Where I differ is that Beatrice and Eugenie are no longer children. They're women in their thirties and have had many years to establish their own identities and make their own decisions. I don't think they should be condemned simply because of Andrew, but I also don't think they should be treated as though they have no agency.
Your friend and her brother were innocent victims of their parents' wrongdoing. In the York sisters' case, some of the criticism directed at them relates not to Andrew's behaviour, but to choices they themselves have made as adults. So, for me, the situations aren't entirely comparable.
I can have sympathy for the position they were born into while still believing they should be accountable for their own actions, just like any other adults.