The existence of magic does not, as Hermione had once upon a time hoped, eliminate the class problem.
Hermione Granger grows up part of the local gentry in Islington. Her father and mother meet during the war, serving as doctor and nurse on the same side, and because they are on the winning side, when her father is honourably discharged, he marries Helen Smith and builds a modest but comfortable abode in Islington. Hermione Granger does not grow up filthy rich, by any means, unless you count her parents' passion for reading that the instill in their only daughter, and their wealthy book collection that no local doctor should afford to have. Hermione Granger grows up with delusions of grandeur, precisely because her parents never teach her that she shouldn't: she wants to go to university (Cambridge, of course) and to become a doctor (the first female one in the country if possible); she has no talent for embroidery and piano playing, despite the many lessons she receives, and she is not spoilt enough to think that all her problems will be fixed by getting married.
Finding out that she is a witch is the turning point in Hermione's life, in a way. She is whisked off to a magical school, where she can learn to control her powers so they do not harm her loved ones, and she attends it believing that she will find a new world to belong in. She is somwhat wrong.
In the wizarding world, it turns out, there is one more category that creates a separation between class: blood. People like Hermione - born and raised by Muggles, not surrounded by magic - are low class citizens, treated mostly like children in some ways. Poor muggleborns, they don't know about this ritual, they never read this children's book, they don't understand the marriage rules! It's eminently frustrating, for her entire life at Hogwarts, to be condescended to despite performing well in class. To be questioned for being better than those older families at magic, when all their propaganda says that muggleborns are dumb and weak.
When, after finishing her fifth and final year, she is shown the door, Hermione does not feel any closer to belonging in the wizarding world than she did in the muggle one.
Nothing short of a miracle rescues her from returning to her parents' home to become a solitary, reclusive spinster; Lady Alice Longbottom requiring an educated young lady to take notes during her literary salons. Hermione has no idea how she ends up employed by Lady Longbottom - could it be that her son mentioned her, from when they were in Hogwarts together? could it be that maybe Professor McGonagall had recommended Hermione to the Dowager Longbottom? - but regardless of that mystery, she has been in their employ for over a year now.
It shouldn't come as a suprise when, upon entering the reading room on Monday morning, she finds Neville sitting in her favourite armchair, reading a book on magical plant care that Hermione found last winter in Paris. After all, Hogwarts is finally over, and by her calculations Neville will have finished it. Sure, there is that initial bitterness, over how purebloods are allowed to further their education for an additional two years, whereas muggleborns are expected to sod off on five years of condescension alone. But it is also Neville, who was a friend to her for those five years, and she's not been able to write to him (having no owl of her own) before to let him know.
(Though maybe his mother did inform him. Or maybe he knew.)
"Ah, the prodigal son is finally home, I see," she says by way of greeting, with a cheekier grin than she would've afforded around any of their other classmates.
1800s, rags & riches