The Black family is one that has a long history of less-than-favorable viewpoints on any witch or wizard who isn't pure blood, and a clip from Hogwarts Legacy show's the school's then headmaster, Phineas Black, shares his family's views. Black's views on half-bloods isn't exclusive to his family, with many of the notorious wizards and witches believing the wizarding community's bloodlines should be kept as pure as possible, the most infamous of these being Lord Voldemort. However, Black's own views appear to be driven from a place of selfishness as he looks to cement his place in history as headmaster of Hogwarts.
Phineas Black is Hogwarts' headmaster when the player's character first arrives at the school during Hogwarts Legacy, with Professor Matilda Weasley serving as his de-facto number two. Over the course of the game, it becomes clear Black views his job as a source of potential prestige for himself and his family given Hogwarts' reputation as one of the most famous wizarding schools in the Harry Potter universe. Despite this drive, he shows little care for the academic side of his job and relegates anything regarding the staff and student-body to Professor Weasley.
Black's ignorance toward the needs of Hogwarts' students can be seen in how he addresses them over the course of the game, such as the announcement of a Quidditch ban at the start of the player's first year due to an "unfortunate injury" the year before. It is one of many instances where Black's apparent contempt for the academic side of his job comes through over the course of the game. However, his true feelings for non-pure blood students comes to light in a clip posted to the HarryPotterGame subreddit by Reddit user Phalaenopsis83 showing Black walk up on a pair of Slytherin students bullying a Hufflepuff.
The interaction between Black and the students is just a small taste of the disparaging views the headmaster's larger family has toward any witch or wizard who isn't pure blood. He isn't as overt as others in his family with sharing his bigotry, which players could argue is due to his position as Hogwarts' headmaster. That said, he still manages to inject the interaction with enough arrogance and bigotry to make his beliefs clear along with his selfish drive for recognition during his time as headmaster.
Headmaster Black's views are not limited to his family, though, as the various books and films set in the wizarding world have shown how deep this sort of bigotry runs. Harry Potter encounters it among his peers, most notably in Draco Malfoy's overt bigotry aimed at Harry's close friend and fellow Gryffindor, Hermoine Granger. Sirius Black was one of the only members of the family to buck this trend given his close friendships with Lily and James Potter. This led to him becoming Harry Potter's godfather, being sorted in Gryffindor House instead of Slytherin, and ultimately running away from home to escape his family's hateful views.
Hogwarts Legacy is currently available for PC, PlayStation 5, and Xbox Series X/S, is scheduled to release for PlayStation 4 and Xbox One on May 5, 2023, and scheduled to release on July 25, 2023, for Nintendo Switch.