Spoiler Alert! This article or section contains details not covered in the anime. Do not proceed unless you wish to be spoiled.
Family[]
Kaguya Shinomiya[]
Kaguya Shinomiya is his little sister. Although he doesn't appear to care much about her, he and her are both in similar positions, having a weaker claim on the family name than the older sons of Gan'an. As such, he understands her almost better than anyone else and finds her to useful for his own ambitions.
Un'yo is surprised however to see the recent developments of his sister, where she has become more forgiving and humane, whilst he remained the same cold-hearted individual.
Kaguya is the only person so far to whom Un'yo has shown genuine respect, as he treated her consent on the matter of recruiting Ai Hayasaka to his side as a vital part of his plan. It should also be noted that he does not enforce his will on her and didn't punish her for hitting him.
As of Chapter 242, it has been told that Un'yo didn't see Kaguya as the illegitimate child of his father like the rest of the family did, and raised her like his own sister. He said that he raised Kaguya just because she was an important pawn he could use, but Shirogane knew he did have a soft spot for her.
Oko Shinomiya[]
Oko Shinomiya is his oldest brother. Un'yo has expressed dislike and agitation at Oko's existence. He scoffs at the idea of him becoming the next Head of the clan and mocks him for not possessing their father's charisma. When accused of treachery, Un'yo tells Oko he was never on his side to begin with. Un'yo's disdain for his brother runs so deep that he would rather team-up with the Student Council to help thwart Oko's plans than let him take Gan'an's position.
Un'yo's dislike of his brother stems from a variety of reasons. One part of it is that, just like Kaguya, Oko considers him a 'half-breed' and a 'potential threat' and thus had Nao Hayasaka preform the duty of a double agent to get key intel on him when he was young. It is likely due to that event that Un'yo gained such a pessimistic outlook on not just life, but the Shinomiya family itself.
As Oko himself explains in chapter 259, the Shinomiya siblings never had familial bonds due to the circumstances of their upbringings. They don't see each other as family but as political assets to be used or crushed.
Servants[]
Ai Hayasaka[]
Un'yo detests Ai Hayasaka for her treachery against his sister and her role in assisting his older brother Oko with his plans. He doesn't regard her as anything more than a filthy rat who could be useful for his plans. When the President decided to go up against his older brother, Un'yo didn't have much qualms about enlisting Ai's help, suggesting that he currently feels a sort of neutral indifference towards her.
Nao Hayasaka[]
Nao Hayasaka was his personal valet in their younger years. They had a strong bond of trust which was ruined by Oko's manipulations. Un'yo's exceedingly negative attitude towards people he deems to be traitors seems to stem from Nao's betrayal of his trust.
When Nao suggested that if they had trusted each other a bit more maybe things could have had a different outcome for them, Un'yo was disgusted.
Others[]
Shijo Family & Hayasaka family[]
He views them as traitors and holds immense disdain towards them.