We see Jason's default class dynamic challenged again in "Solarium". Jason's fear of being posh is one of the reasons he publishes his poems under a pseudonym. This idea of poetry being high class is underscored when we meet Eva. She's the first person he ever talks about his poetry with, and she's ridiculously, ostentatiously posh. Her personality and way of living are so far removed from all that Jason has experienced in Black Swan Green that they makes him feel comfortable talking about art, beauty and classical music. Perhaps it is because of her influence that Jason is so receptive to "Moonlight Sonata" later.
But it's not as simple as "part of Jason's coming-of-age is learning to not be afraid of being posh". "Embrace your privilege" would be a weird moral. No, class plays a major role again in "Knife Grinder", and the dynamic is turned on its head again regarding the gypsy camp. The language the people of Black Swan Green use at the Village Camp Crisis Committee specifically attacks the gypsies for being uncultured, unlearned, and poor. They complain about them taking welfare, calling them lazy and beggars. Jason doesn't seem swept up in all this, though. Certainly he likes Mr. Moran, who's a quarter gypsy. And when he gets to the gypsy camp, he finds them decrying settled people in exactly the same ways.
Ultimately, I think Jason's observation about how both the gypsies and townspeople "wanted [the other side] to be gross, so that the grossness of what they're not acts as a stencil for what they are" is vital. Class doesn't necessarily dictate differences in people; people use class to divide themselves. Maybe at the start of the book Jason could have concluded that people with the least privileged upbringing make the worst bullies, but when Ross Wilcox is knocked out of commission he's immediately replaced by Neal Brose, whose upbringing is pretty much the negative referent of Ross's. I like that Jason's development in the book regarding class isn't so much of "one understanding falls away for an opposite one" so much as "a facile understanding gains nuance".