These mostly apply to prejudices at Hogwarts, not real life
Gryffindors: Hufflepuffs and Gryffindors get along very well. They're the two most amiable houses together. That being said, some Gryffindors think that Hufflepuffs are boring and "a load o'duffers," but the two houses generally get along.
This is implied in The Goblet of Fire. It's suggested that the Hufflepuffs would have supported Harry if Cedric hasn't also been chosen.
Hufflepuffs and Gryffindors are both fun-loving and not too serious, but Hufflepuffs may think that Gryffindors are too reckless. (See Hufflepuffs at Ilvermorny)
Generally, Gryffindors and Hufflepuffs get along because they're usually very friendly people.
Some Gryffindors may be arrogant, but Hufflepuffs don't think Gryffindors are any more arrogant than Ravenclaws can be about their intelligence or pureblood Slytherins can be about their heritage.
(Hufflepuffs get really sick of Gryffindors bragging, though)
Slytherins: Hufflepuffs don't get on quite as well with the Gryffindors rivals as well as they get on with the Gryffindors themselves. However, the Hufflepuff/Slytherin relationship is a lot of fun and usually better than the Hufflepuff/Ravenclaw one.
The reason that Hufflepuff and Slytherin don't always get along is because what many Slytherins say is "funny," Hufflepuffs say is "mean."
For example, both Hufflepuffs and Slytherins wore the "Potter Stinks" badges. This isn't surprising, considering that Slytherins and Gryffindors are rivals and Hufflepuff was bitter about Harry being chosen.
That being said, the "Potter Stinks" badges were accepted by nearly all of Slytherin house. Slytherins thought they were funny.
Some Hufflepuffs thought they were funny, but others thought they were unnecessarily harsh.
Hufflepuffs and Slytherins can be great friends, as both houses appreciate jokes and sarcasm. But when a Slytherin "crosses the line" with a joke, it can turn ugly.
Ravenclaws: This is the most shaky relationship. The two houses are often quidditch rivals, but they're usually competing for second place.
Hufflepuffs and Ravenclaws don't dislike each other, but the relationship is kind of awkward.
Really, many Hufflepuffs and Ravenclaws don't find a lot of things in common to do. Hufflepuffs can be smart, but studying with a Ravenclaw isn't usually a lot of fun for them.
Together, the houses lean towards more cautious, so they don't often do adventurous activities like the Gryffindors or pranks like the Slytherins together. Neither one wants to be the first to jump.
The two houses often struggle to find things that they both enjoy doing.
Don't get me wrong, there are definitely things that both houses like doing.
But their favorite activities just usually aren't things that both houses would enjoy.
Hufflepuffs also think that Ravenclaws can be kind of snobby, and that doesn't really help house relations either.
Recap:
Hufflepuff/Gryffindor: Get along the best, and are usually friendly
Hufflepuff/Slytherin: Usually get along, but Hufflepuffs are more easily offended.
Hufflepuff/Ravenclaw: Get along, but don't typically interact a lot. Don't always enjoy the same things.
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Why Hufflepuffs are Awesome
FanfictionYou might belong in Hufflepuff, where they are just and loyal. Those patient Hufflepuffs are true and unafraid of toil. (And really cool. Plus, we have cookies.) **Companion to Why Slytherins Are Awesome** (completed)