"What you see from this thread is entrenched perspectives towards private school students, nothing going the other way."
That’s because the privately educated enjoy unearned privilege. Through their parents’ money and the type of education it purchases, they have an easier ride to: good A-level grades, a place at a good university, extracurriculars, cash to live in nice accommodation, and, often through personal and parental contacts, work experience and future employment.
This contravenes many people’s notion of what is fair, irrespective of the fact that private schools are currently legal (which, IMO, they should not be). This dynamic is not in play the other way around.
There’s also, in my experience, often an unattractive and overbearing sense of entitlement among the privately educated, a superficial "confidence" and bearing that can, for instance, win over a job interviewer when that candidate is not necessarily the best one. Of course, few parents of the privately educated, especially if they were privately educated themselves, will acknowledge or even recognise this. To them, they are simply "normal" kids. This is akin to how many white people often can’t recognise their own privilege.
At university, in my experience at least, the privately educated often have more resources: perhaps a car; a higher weekly budget for entertainment, etc.; parental cash to live in better accommodation; parental cash for holidays, etc. This means the privately educated can fit in with those less well resourced if they wish to, but, again, it doesn’t always work the other way around. That is why it is understandable and entirely rational for some state-schooled kids (the vast majority of whom, outside of a few Home Counties bubbles, are not as wealthy as the privately educated, despite comments to the contrary above) to be wary of situations and universities with a large overrepresentation of the privately educated. If you are state-schooled and not from a wealthy background and attend a university that has 30% of its student body privately educated, you are reducing the pool of people you are likely to get along with, or perhaps more accurately, share a similar lifestyle with. It’s not simply an irrational "fear" to consider this.
That said, university is a great opportunity to make new friendships, and these may well include some between private and public school kids. I would actually encourage state-schooled kids to meet at least some private-schooled kids, as the state-schooled will realise they are likely brighter and harder-working if they have gained a place on the same course as a privately educated kid but without a leg up purchased by parents. This, of course, sadly, doesn’t counter the fact that post-university kids from wealthier families often unfairly scoot ahead as they can secure work experience through contacts, subbed through internships, and draw on parental contacts for jobs.
Private education creates inequality. The suggestion in the posts above that we should somehow be blind to this inequality is just another way of maintaining the status quo to the advantage of the privately educated, driven by an adherence to conservative ideology. Britain is already one of the most unequal Western ‘developed’ countries, yet greater equality is key to creating a happier, better functioning society (see "The Spirit Level" by Pickett and Wilkinson and a vast amount of academic literature for evidence). As I mentioned upthread, I encourage my DC to get along with anyone but to recognise privilege (including their own) where it unfairly manifests itself.