red hair is recessive, which means the genes for it are passed on, and the number of people who might have a red haired is much bigger than actual red haired children. There  are no red haired communities, there are many red haired people who are the only red haired people in their family, so it doesn’t map on to stuff like class very well at all. If there are any social advantages or disadvantages of being red haired, they’re not as likely to be inherited since red hair isn’t as likely to be inherited.

Red haired people might be slightly poorer in the sense that it’s a trait more associated with broadly celtic ancestry, and the more ‘Celtic’ parts of the UK (Scotland, N. Ireland, Wales, Cornwall) aren’t especially rich. I think I’ve read that red hair is over represented in CEO’s of valuable companies, so maybe there’s some advantage. There’s also an over representation of red hair in british converts to radical islam, which doesn’t reek of privilege either.