One possible reason could be for his safety. Konoha is a well - protected village with many skilled ninja. She might believe that leaving him there would ensure he has the best chance at survival and growth as a ninja. Also, she may have some mission or obligation that forces her to leave him behind, perhaps something related to the greater good of the village or the ninja world in general.
It could be related to her own power or abilities. Suppose her powers are unstable or attracting unwanted attention. In that case, she may fear that being around Naruto would put him in danger. So, she decides to leave him in Konoha, a place full of ninja who can protect him while she tries to deal with her own issues on her own.
Maybe she feels that she's not a fit mother at that moment. She could be dealing with her own personal demons or traumas that make her think Naruto would be better off without her direct presence. In the fanfic world, there could be some dark secret she's trying to protect Naruto from, and she thinks leaving him in Konoha, where there are people like the Third Hokage to look after him, is the best option.
One possible reason could be for Naruto's safety. Maybe she has to go on a dangerous mission and believes Konoha is the safest place for him. Another reason might be that she is forced by some powerful enemies who threaten Naruto's life if she doesn't leave him in Konoha.
The relationship between Konoha and the Uzumaki clan might be further strained. With Kushina leaving, Konoha would lose an important link to the Uzumaki. And other Uzumaki members might see this as a sign that Konoha is not a safe place for them.
In a 'naruto and kushina leaves konoha fanfic', perhaps they leave due to a threat to Naruto's safety that the village can't fully protect against. Maybe some secret organization is after him and they feel they have no choice but to go into hiding outside Konoha.
One possible reason could be to protect Naruto from the hidden threats in Konoha. Maybe she discovers some dark secrets or plots within the village that she believes will endanger Naruto, so she decides to take him away.
Naruto would probably feel abandoned at first. He might become more withdrawn and have trust issues. But as time goes on, he could grow stronger out of a need to prove himself. He may also form closer bonds with his friends in Konoha, like Sasuke and Sakura, as they become his new family in a way.
They might leave because of a prophecy. If there was a prophecy that Naruto would bring destruction to Konoha or that Konoha would bring destruction to Naruto, Kushina might take Naruto away to prevent it.
The first consequence could be a breakdown in the village's unity. Naruto is seen as a hero in Konoha, and if he turns against it, many of his supporters might be confused or even follow his lead. This could lead to internal strife within the village.
Well, if Naruto and Kushina left Konoha in fanfiction, it would change a great deal. Naruto would not have the same relationships with his friends like Sasuke and Sakura. He might develop different fighting styles as he wouldn't be trained by the same people in Konoha. Kushina, being a strong kunoichi, could train Naruto in her own unique ways. And their departure could also cause a stir in Konoha, with some people trying to find them and others realizing the mistakes they made in how they treated Naruto and his family in the past.
In some fanfics, Naruto might leave Konoha as a child because he feels ostracized. Since he's the jinchuriki of the Nine - Tails, many villagers fear and shun him. He could get tired of the constant cold shoulders and decide to leave in search of a place where he'll be accepted.
One possible reason could be a mission. In many Naruto - related stories, missions often take characters away from their families. Naruto might have received a highly important and dangerous mission that requires him to be away from Kushina for a long time.