Perhaps in a fanfiction, Sasuke discovers a new and extremely dangerous power that he can't control and it starts to endanger Konoha. Naruto tries to stop him but in the heat of the battle, accidentally kills him. Overwhelmed with guilt and feeling that the village will never understand, Naruto leaves. But this is a very different take on their relationship and the Naruto world as a whole.
In a more convoluted fanfiction plot, there could be a conspiracy within Konoha. The elders or some secret organization within the village wants Sasuke dead for some reason. They manipulate Naruto into believing Sasuke is a traitor and a danger. Naruto, being the naive and trusting person he can be at times, falls for it and kills Sasuke. Realizing he's been used, he then leaves Konoha in disgust.
Maybe they leave because of a conflict within Konoha. There could be political unrest or a group within the village that they don't agree with. They might think that leaving is the only way to avoid getting involved in something they don't believe in or to protect the village from the inside out in their own way.
Another reason might be that Naruto is seeking a greater purpose. In the fanfiction, his 'godlike' state could make him realize that there are threats out there that he can't face while being tied to Konoha. He may leave to protect the world on a larger scale, believing that he can be more effective away from the village.
They may leave to investigate a mystery that has long been ignored or covered up by Konoha. This could be related to the origin of certain powerful jutsu or the real history of some important clans. Their departure from Konoha is a way to break free from the village - imposed limitations on knowledge and seek the truth on their own.
One reason could be to seek a new life away from the constraints of Konoha. Maybe they feel that they can't fully grow or explore their potential within the village. Another reason might be to protect Konoha in their own way. They could believe that leaving and dealing with threats from the outside would keep the village safer.
With the villagers of Konoha, Naruto was once seen as a hero. But his leaving could cause mixed feelings. Some might see it as a betrayal, while others might respect his choice. Fem Sasuke was always an enigma in Konoha. Her leaving might be seen as expected by some, but for those who hoped she would fully integrate into the village, it would be disappointing. And as they journey outside Konoha, they will meet new characters, and their relationships with them will be based on their new identities as outcasts from Konoha.
Well, it could be that Sasuke decides to join Naruto in leaving. They've always had a complex relationship. Maybe Sasuke sees Naruto's reasons for leaving as valid and decides to support him, which strengthens their bond.
They could leave because of a prophecy. Some ancient prophecy might state that they need to leave Konoha to fulfill a greater destiny elsewhere. So they trust in this prophecy and leave their home.
Maybe they leave to find a better way to protect Konoha. They might think that by exploring the outside world, they can gain new knowledge and powers that will be useful for their village in the long run.
Well, it would be a big loss for Konoha. Naruto is a powerful ninja, and his absence would mean one less strong fighter to defend the village. Ino, too, has her unique skills in mind - related jutsu and communication. Their departure might also lower the morale of other ninja, especially those who were friends with them or looked up to them.
It would be a huge blow to Konoha. Naruto is a hero in the village, and his departure would leave a big leadership void. The villagers would also lose a great source of inspiration. Hinata is from a respected clan, and her leaving would also have an impact on the clan's standing in the village. Morale among the ninjas might drop as they see two important figures leave.