Greenleave, what you say is familiar.
I think DD was 12 when she came home as complained that another girl (again with a banker mum) was "racist towards the English". Slightly earlier she had complained that everyone else came from "somewhere", whilst she did not, as if being native was a negative. She had more of it at an extra-curricular where English-identifying kids were in a minority. Part of the problem was that we were content to let the school do the work, and so, as long as there were no complaints from teachers, not get involved in supervising homework etc. Essentially our "attitude" was different to many of her peers. It was quite obvious that her peers, and their parents, considered her less bright (she was at a "less academic" school than many of them) and quite probably "not appreciative of hard work".
Its worked out fine. SS has proved a bit of a tortoise, and at the end of her schooling has clearly caught up with these peers or even overtaken them. The one pity perhaps is that she has only started to shine in maths in the last couple of years. At GCSE level the kids with maths "homework clubs" did better. Her teacher now says it is a real shame she has not taken double maths, and I think she agrees. But till maths got harder and others started to struggle despite hard work and external help, she did not know she was any good.
DD came about 800th on the Tiffin wait list. (No tutoring, just some VR and non VR practice a couple of months before the test.) Her A level performance will be better than the Tiffin average. However she was lucky she could go to a good school, in our case fee-paying. (The state alternative she was offered was worryingly poor, and you don't seem to be able to get into our nearest state school unless you are a Cameron or a Gove.)
Looking back and knowing what we know, if we had had been offered a place, would we choose Tiffin? Its difficult. There would be parents like Greenleave who believe that the "English" (and I agree she is probably talking about culture not colour) are essentially lazy, and these attitudes will rub off on their children. I would also worry that DD would be outshone, not because she was not bright enough, nor because she did not work hard enough, but because her peers were working so much harder. I would have wanted more balance in her life.
I suspect that I might have followed the example of affluent friends, who sent their boys to a super-selective grammar, but not their very bright daughter, who went to a private school on a major scholarship. I don't know about Tiffin, but have worked with pupils from another all-girls South London school, where one concern from "pure/white English" pupils was that their Asian friends were not allowed to mix with them outside school. Presumably again because of concern about "attitude".
I suppose the main thing I would is for my daughter to emerge from her childhood knowing she is "good enough" regardless of her colour or cultural background. Would Tiffin deliver this? I don't know. Would KGS deliver this? I think so. The girls DD has met from there have been lovely, well rounded and straight-forward. And importantly DD has no idea how clever any of them are. KGS gets good results for its selectivity, especially given Tiffin will have creamed off the top of the cohort, yet seems to allow kids to find their natural level.