The setting of the story "The Doll's House" is very influential to the plot. The story is set in New Zealand during the early 1920s, when the country was still a British colony. As such, the traditional British dynamics would be expected to resonate in New Zealand society, where there was also a huge gap between the rich and the poor, and where rules applied to the upper and lower classes differently. In other words, New Zealand, as a British colony, also had the same classicist society as England.  

This setting would explain why the Burnell sisters, and their peers in school, were so aware of how different the Kelvey girls were. In fact, they were aware of everything about the Kelveys, from what their mother did for a living, to who their father could be. This shows how typical it was for the rich to look down on the poor at that time and place. It also explains Aunt Beryl's horrid treatment of the Kelvey girls, who are literally treated like vermin. 

The setting is also the reason the Kelveys and the Burnells are coexisting in the same school. The fact that they live out in the country means that there is only one school for everyone to attend.

...the school the Burnell children went to was not at all the kind of place their parents would have chosen[...] It was the only school for miles. [...] all the children in the neighborhood, the judge's little girls, the doctor's daughters, the store-keeper's children, the milkman's, were forced to mix together. 

Had the setting been in the city, chances are that the Burnells would have attended a school for the upper classes while the Kelveys would not have been seen near such a place. Hence, the particular setting in the countryside, as well as in New Zealand in the 1920s, are important backdrops for the plot to unfold.