Horcrux held the essence of Voldemort’s soul. As we saw from Tom Riddle’s diary, it will act in its own self interest and it will defend itself from elimination.
Hermione, Ron, and Harry were trying to catch and destroy Hocruxes. The Hocrux sensed this and used preventative measures similar to when they obtained the Gryffndor sword.
When Tom Riddle’s diary was with Ginny, it acted attentively and invested in Ginny’s problems then used her to open the Chamber. From there it almost possessed her soul if not for Harry.
The Locket used all their concerns, frustrations, and doubts about their journey against them. It caused them to fight among each and take much longer to complete their mission that was against the locket’s best interest. Think about the decoy story the diary told to Harry so he would be distracted from what was really going on with the chamber of secrets.
Dolores Umbridge held the Locket for a short period of time. Based on the Ministry of Magic pamphlet propaganda Umbridge was making at the time (mudbloods and the dangers they pose to a peaceful pure blood society ) It is doubtful that the Locket would want do anything against her best interest. If anything the Locket may have been channeling her anti-muggle hatred and expanding on it.
Dolores Umbridge complemented Voldemort’s essence well so there really was no negative effect just an expansion on how Umbridge already acted. With the new Ministry, she was capable of expanding on muggle-born hatred and actively create kangaroo courts against muggle-born and half-blood wizards. Her legislation was also crueler on non-wizard kind such as goblins, house-elves, and centaurs. We do not really know how much of what she did was her and how much of it was enhanced by Voldemort’s soul.