Warning sort of because you may find some of this stuff spoilerish, and this is for Wen who I don't think has made it to the fourth book. I don't give anything away, but you will learn of some plot devices, so proceed at your own risk.
This isn't going to be like a real post, but I certainly invite comments to the following. In my far too numerous reading of Harry Potter, the different ways J.K. Rowling has approached issues of race/class have always sort of stood out. This isn't an opinion post so much as it is things I've noticed. In rereading the series, for the first time in its entirety, I'm only up to book four, though I'm nearing the final task of the Triwizard Tournament.
The two observations are both from this book, The Goblet of Fire. This is the book in which Hermione starts S.P.E.W. the Society for the Promotion of Elfish Welfare. She insists on helping the house elves of Hogwarts to better themselves by demanding pay and time off as well as regular clothing. For all Hermione's insistence on helping them, they more vociferously deny that they want the perks she feels they have a right to. They claim they are quite happy, yet one can't deny that they are a species based on servility. It brings to mind suggestions during the years of slavery, made by some slave owners, that they were doing a service to the black people they owned, that they were happy and fed and doing what they were good for.
In book four we also meet the blast ended skrewts. They are seemingly pointless creatures with both a sting and a sucker as well as rocket propulsion. At one point Hermione is quite willing to squash roughly a hundred of them and kill them having tired of Hagrid's lessons that involved suffering the skrewts' stings and burns while trying to feed and care for them.
At another point, Cornelius Fudge and Professor Dumbledore are discussing the appearance and subsequent disappearance of a particular character, an incident which happened near the Beauxbatons carriage. Hagrid and Madame Maxime, due to an issue of parentage/genetics, are discussed in terms of their propensity toward violent behaviour. Fudge insists that, because of this, Madame Maxime is a likely suspect in the incident with Dumbledore insisting that it isn't very likely. Fudge suggests that, due to Dumbledore's relationship with Hagrid, he may be prejudiced to the condition that Hagrid and Madam Maxime share. Dumbledore suggests that it is Fudge who is prejudiced.
These aren't the only instances in which I've run across the theme, though they are the ones in mind currently. Combined with the theme of racial purity inherent in the pure blood of certain wizarding families versus the muggle borns/mudbloods they despise, the subject of race and even class are prominent themes. It's a subject that I noticed throughout the books, but rereading them is really shining some lights onto things I missed before. It isn't a subject that's preached or hammered, and I've certainly found it interesting. It's certainly more interesting than being scared that children who read HP will turn into witches and wizards and stop loving Jesus.