I suspect that those who are saying that they, or their children, have no issues with non-uniform in relation to brands and bullying are perhaps those who have been able to afford to dress their children in a way that does not stand out in such an environment.
As I have said on here before, I was on a 100% scholarship to a 'posh' girls' boarding school. Uniform up to O-level, non-uniform but dress code for sixth form. I was year-accelerated, very bright, and came from a MC but poor-as-church-mice family (I put on a fair amount of weight in my first term, simply because I wasn't used to having the amount of food that the school considered 'normal').
Uniform years were fine - there was a second hand shop and all my clothes came cheaply from there. OK, my weekend 'home' clothes were not like other people's, but we only wore them on at and Sun afternoons, so it wasn't an issue, and there was no bullying or other comments.
Sixth form was a nightmare. I could not possibly have asked my parents to buy me the kinds of clothes that were 'normal' for other people, so I continued to wear home-made skirts and 'knitted from unravelled wool from outgrown items' jumpers, except for the one 'shop' jumper that my grandparents gave me each year for Christmas. Was I bullied? Oh yes. My 'differentness' was hugely emphasised by my clothing.
In non-uniform contexts, I suspect that those who have 'what is expected', and those who are able to buy 'something similar to what is expected, maybe just one or two items but not them all' are OK. Those who genuinely cannot manage ANY of what is expected may be a very small subset - clothes are cheaper than they were when i was a teen - but genuinely DO suffer. The effect may be particularly bad for those who are already 'on the edge' of social acceptability within their peer group through other types of 'difference' - and it is these vulnerable kids, not the 'unvulnerable majority' that we should be seeking to nurture.