Copied from someone's Reddit post so you don't have to go there:

I made a list of examples of racism, prejudice, and stereotypes in the HP books.

1. Kingsley SHACKLEBOLT is black, tall, bald, with a deep voice, and has a single gold hoop earring. He is wise and gentle.
   (References: Slavery; black men are tall and physically hyper-masculine; the "magical negro"/"numinous negro" trope of wise, purely magnanimous black men; stereotypical black-dude fashion.)

2. Dean Thomas is black. He is described as being taller than Ron. Dean's father left him when he was young. His best friend is Seamus, an Irish kid.
   (References: Black people are tall; black dads abandon their families; black and Irish people both used to be on the bottom rungs of western society).

3. Cho Chang is Asian. She is in Ravenclaw, and is very focused on her studies. She is a seeker and Rowling specifies that the best seekers are usually small and light. (References: Asian people being particularly academic, and being small and slender)

4. Seamus Finnigan is Irish. He is skilled in pyrotechnics, had several "incendiary mishaps" in his first year, and McGonagall chose him to blow up a bridge during the battle of Hogwarts.
   (References: Irish Republican Army terrorism/bombings).

5. Fleur is French. She is beautiful, ultra-feminine, and her grandmother was a LITERAL INHUMAN SEDUCTION MONSTER THAT TURNS INTO A HARPY WHEN ANGRY aka a Veela.
   (References: French women being particularly feminine and sexual; beautiful women being two-faced and less human).

6. The mascot for the Bulgarian Quidditch team is a Veela.
   (References: Eastern European women are highly sexual seduction monsters)

7. Filch, a "squib", is disabled by wizard standards. He is a janitor and an angry, spiteful, miserable person who enjoys causing pain and aligns himself with whoever will benefit him most.
   (References: Disabled people can only do menial/manual labor; disabled people are mean/amoral.)

8. Goblins are greedy, short, intelligent, have long hooked noses, speak their own language, sometimes wear special hats, run all the banks, and are very focused on collecting debts.
   (References: Various jewish stereotypes; jewish cultural traditions such as speaking Hebrew and wearing yarmulkes)

9. Werewolf-disease (lycanthropy) has been explicitly confirmed by Rowling to be about HIV/AIDS. The two werewolf characters have strong, nearly uncontrollable urges to attack others and turn them into werewolves. One of them takes medication to reduce his urges. The other EXPLICITLY TARGETS CHILDREN, KILLING SOME AND TURNING OTHERS INTO WEREWOLVES.(References: Gay people are sexual predators (because in the 80's and 90's in popular culture, HIV/AIDS = being gay); gay people are hyper-sexual with poor self-control; gay people recruit children and turn them gay; being gay is a disease and affliction, responsible gay people repress their gayness.)

10. Rita Skeeter is woman who is described as being unattractive, having manly characteristics, and dresses in a way similar to a drag queen. She is a gossip, and is dishonest and duplicitous. She hovers in private spaces, and changes her body in order to spy on children. Skeeter is a nickname for mosquito, she is a literal pest.(References: Trans people are predators; trans people intentionally trick others / transition for malicious purposes; LGBTQ people love spreading celebrity gossip.)
    Apparently Rita's appearance also resembles a character played by a male comedian, down to the hair and the bedazzled horn rim glasses, though I forget his name.

edit:

11. House elves love being enslaved and working in people's houses.
(References: slavery benefits enslaved people. Enslaved people are happy to be enslaved. Possibly: house-slaves in particular enjoy and benefit from slavery (as opposed to field slaves.))

12. Women are depicted as entrapping men into relationships with love potions and love spells. Men are not depicted as using these things. I'm not sure exactly how to phrase this, but it feels...wrong to me.