I went to ten schools with a wide variety of social stratification. Whilst most generalisations will have exceptions, of course, I found a distinct tendency for the posher lads to be dodgier, perhaps from a feeling of being less vulnerable to authority. The extremes of variations in the girls was much less, to the point of being largely negligible.
I do think your surroundings have some effect, in both directions - the results can perhaps be steered a bit by yourself, but you can only work with what you have available.
My father had moved up to Dublin from Laois, finding work as a barman - then he took it into his head to join the RAF - we went to Scotland, then three years in Malta, with my first year of school there, then to the Cotswolds, like living in a picture on the top of a biscuit tin. Around England from there, then, most important of all, three years in Cyprus as a teenager - that made me what I am. Downhill from there, though - back to Lincolnshire - like being put into an induced coma...
After that, I accidentally went to an excellent college and worked in a factory that was like being in a sit-com* all day.
If we'd stayed in Dublin, I would be somebody else altogether. I often wonder about that.
At the poshest school I went to, pretty much the only lad I trusted for my year there was, like me, sent by the council, and the school put up with us, or they didn't get the subsidy money that we brought them. We were required to state what our fathers worked at. They weren't hugely happy with my father not being an officer, but they actually refused to record his father as 'farm labourer', glossing over it by describing him as a 'farmer', which looked so much better.
*If you can find any episodes of The Gaffer, with Bill Maynard, it is a wonderful caricature of the state of British industry in the 1980s.