CJB remember that when you've met one private school educated student, you've met ....one private school educated student and they're all very different to each other.
DS1 and DS2 - brought up from the start by me - their single mum - were on means-tested bursaries at their private school and we were never able to afford things like foreign family holidays when they were growing up, let alone own a yacht or two and neither has ever even been on a plane or travelled ....and we don't even own a Dyson (LOL!).
Most of the other students each of them has met at their colleges, have been state school educated and lots are from very deprived areas. DS1 (C) particularly has had to listen to quite a lot of misguided ideas about 'posh private school students' that bear no relation to his own background and his own DOS making regular 'put downs' about private schooling. He also overheard a group of first years talking about the single Etonian at his college and people were saying "...and I'm surprised to see the Etonian seemed fairly normal actually! ", as if just because the boy was from Eton, he'd be a different 'species' when of course lots of Etonians are also on means tested bursaries too. You just never really know about people's origins unless they feel some need to tell you.
At DS1's college, either no one has mentioned coming from 'wealth' or instead has made a big deal of 'regularly experiencing knife crime right outside their door at home' and how they don't want Cambridge to 'change' them and want to remain faithful to their roots. If there's any 'prejudice' it's been against private school students not the vast vast majority who are state schooled - and of course there are so many different varieties of state school too, in any case.
I just think it's a shame that any student makes assumptions at all and puts any one group into a special category, when each is unique and anyone who needs to discuss their two yachts or alternatively, their knife crime neighbourhood is missing the point of seizing the opportunity to mix with an eclectic bunch of bright minds, regardless of financial circumstances.