What happens when people born and raised in cities grow more and more contemptuous of people living rural lives?

I think the issue you’re concerned about is already here but the other way around. If you look at polling data rural individuals express high levels of fear and contempt towards urban areas and, somewhat amusingly, also believe that urban areas are net recipients of their money when the reality is HUGELY the opposite.

I think there’s some antisocial traits that rural living selects for and so this isn’t entirely surprising and I’m not sure something we can really fix but if your concern is the cultural divide between urban and rural there’s no need to worry about future urban divides when the rural people have been there for a long time. Maybe focus on them?