They could both be tired of the expectations placed on them in the village. Naruto is always expected to be the hero, and Hinata is expected to be a proper clan member. Running away gives them the freedom to be themselves and build a life on their own terms.
Love. Naruto may finally realize his true feelings for Hinata and want to be away from the chaos of the village to be with her in peace.
Hinata might be in danger, and Naruto, being the heroic type, decides to run away with her to protect her. Maybe there's a powerful enemy targeting Hinata specifically, and Naruto thinks the best way to keep her safe is to take her away from the village.
They might run away to avoid a conflict that their villages are about to be dragged into. Naruto and Sasuke, being the powerful ninjas they are, don't want to be used as tools in a war, so they decide to run away.
Maybe he's running away from the pressure in the village. There are always high expectations on him, and he might feel suffocated and need some time alone to figure things out.
They might run away because they want to explore the wizarding world on their own terms. Without the restrictions of Hogwarts or the watchful eyes of the Ministry of Magic.
From a security perspective, Konoha would be weaker. Naruto is a very powerful ninja, and Hinata is no slouch either. Their skills and abilities would be missed. Enemies might see this as an opportunity to attack Konoha. Also, Naruto has been a symbol of hope for the village. His departure could lead to a decrease in morale among the villagers. They might start to feel less secure and more pessimistic about the future.
Maybe for love. They might have fallen deeply in love and want to be away from the prying eyes of the wizarding world.
Perhaps in the fanfiction, Ciel discovers some dark secrets about the Phantomhive family or the underworld they are associated with that are so disturbing that he decides to run away. He wants to distance himself from all the evil and corruption, hoping to find a place where he can be free from all the burdens that come with his family name.
Sakura might be initially shocked but then understand Naruto's decision. She could secretly help them by providing medical supplies. Shikamaru, being the smart one, might predict their actions and try to cover for them so that the village doesn't find out too quickly.
Maybe he feels misunderstood by his family. In many Naruto stories, his family situation can be complex. If he's 'godlike', he might have powers that his family doesn't understand or fears, leading him to run away to avoid conflict or being treated differently.
It could be due to jealousy. Some villagers might be jealous of Naruto's power and Hinata's noble status. So, they spread false rumors that lead to their banishment.
Perhaps they are tired of the constant power struggles and drama. Bella has seen a lot of chaos in the vampire world, and Jasper has been through it for a long time. Together, they decide to run away to find some peace. They want a life away from the battles, the territorial disputes, and the never - ending family feuds. They believe that by running away, they can start anew and build a more harmonious existence for themselves.