There are no real Hogwarts Legacy house differences if you were worried sorting would change anything. You'll get a specific common room but other than that you're not locked out of anything when your house is set. Obviously, each of the four houses comes with its requisite characteristics - brave, smart, evil and miscellaneous - but as far as gameplay in Hogwarts Legacy, your house has no impact on the storyline. So there are no house-specific questlines or objectives to miss out on. You will meet a different set of students initially on your first night at the school but you'll meet everyone as the game progresses.
Does Hogwarts Legacy house sorting matter?
There are no divergent storylines or pathways as a result of your Hogwarts Legacy sorting choice that stem from the result of the Hogwarts Legacy sorting ceremony. So it doesn't matter which house you're in. The only impact will be who you talk to during your first visit to the common room, and where that is in the school. You'll speak to everyone over the course of the game so as well so your house choice just means you meet some sooner.
For example, Slytherin students speak with Ominis Gaunt, Sebastian Sallow, and Imelda Reyes. If you are sorted into Ravenclaw, you'll introduce yourself to Amit Thakkar, Samantha Dale, and Everett Clopton. These conversations won't make you better or worse friends with these characters, and everyone will come up again during lessons, quests, or dedicated friendship missions regardless of whether you meet them on your first night.
Just like whether you become a Hogwarts legacy wizard or witch, house choice is simply a bit of color that makes no real difference. There are dedicated friendship missions for one character from three of the houses: Sebastian Sallow (Slytherin), Poppy Sweeting (Hufflepuff), and Natsai Onai (Gryffindor) but you'll get them whereever you end up. Ravenclaw's Amit also plays a small role in the main mission Lodgok's Loyalty, as well as being useful during your Astronomy Class quest, but if he had a mission thread of his own it ended up on the cutting room floor.
The release of Hogwarts Legacy has been the subject of criticism and debate due to J.K. Rowling's public stance on gender identity, which continues to challenge the inclusivity at the heart of the Harry Potter community. Here is our explainer on the Hogwarts Legacy controversy.