The characters in 'Naruto' would be deeply affected if Naruto dies at birth in fanfiction. Jiraiya would be one of the most affected. He saw Naruto as his protege and the hope for the future. Without Naruto, Jiraiya might lose his enthusiasm for training and spreading his teachings. Tsunade would also be saddened as she had a connection to Naruto through her relationship with Jiraiya and Minato. The Rookie 9, Naruto's friends, would have a completely different dynamic. They might not form as tight a group without Naruto's energetic and positive influence. And the Sannin, as a whole, would have their relationships and legacies altered without Naruto in the picture.
For Hinata, it would be a crushing blow. She loved Naruto so much. She might withdraw into herself at first, overcome with grief. But then, she could find the strength within herself to carry on Naruto's legacy, especially for their son, Boruto (if in a post - Naruto - has - a - family scenario in the fanfiction). Shikamaru, being Naruto's friend, would feel a deep sense of loss. He would use his intelligence to try to figure out what led to Naruto's death and if there was any way to prevent it in hindsight. And the other members of the Leaf Village would be in a state of shock and mourning. Naruto was their hero, and his death would make them question their safety and future without him.
Naruto might also try to remember Sakura in a positive way. He would cherish the memories they had together. He could start initiatives in the village in her name, like promoting medical ninja training more, since Sakura was a great medical ninja. He would slowly turn his grief into a force for good in the village.
Sasuke would be deeply affected. He and Naruto had a complex relationship. His first reaction might be shock and then a deep sense of loss. He might feel guilty for not being there to help Naruto. Sakura would be heartbroken. She had always cared for Naruto, and his death would be a huge blow. She might become more determined to protect the village in his memory. And Boruto, Naruto's son, would be devastated. He would probably grow up with a strong sense of purpose to live up to his father's sacrifice and protect the village even better.
Sakura would be heartbroken. She would probably blame herself for not being able to protect Naruto. She might also start to train harder to fill the void left by Naruto.
Sasuke would be deeply affected. He and Naruto had a complex relationship. He might feel regret for not being there to help Naruto and also feel a new sense of purpose in avenging his friend. Sakura would be heartbroken. She had always cared for Naruto, and his death would make her question the purpose of the ninja life. Haku herself would be in a state of shock and disbelief. She would feel a heavy burden of guilt, knowing that Naruto sacrificed his life for her. She might become more withdrawn initially but then use Naruto's memory as a motivation to become stronger.
Sakura would be devastated. She has been Naruto's teammate for a long time. She might blame herself for not being able to save Naruto. She would probably become more withdrawn and focus all her energy on finding a way to bring Naruto back, even if it's impossible. Kakashi would be deeply saddened too. He has always seen Naruto as a special student. He would likely feel that he has failed as a teacher.
Some fans would be very disappointed. Naruto is a character that represents hope and friendship in the original series. So seeing him die alone in a fanfiction goes against the positive themes of the original. They might not like this dark take on the character.
Sakura would be devastated. She has always seen Naruto as a dear friend and teammate. She would probably blame herself for not being strong enough to prevent his death. Sasuke, on the other hand, might feel a deep sense of loss and anger. He might go on a solitary journey to find out who was responsible.
If Naruto dies at birth in fanfiction, it would have a huge impact on the story's positive themes. Naruto was a symbol of perseverance and the ability to overcome one's past and hardships. His death would mean that those themes would be lost. Also, the Akatsuki's plans regarding the Nine - Tails would be disrupted. They might turn their attention to other 'jinchuriki' more quickly. And characters like Iruka, who played an important role in Naruto's life, would have a completely different story arc as they would not have Naruto to mentor and befriend.
Naruto would be devastated. Sasuke is his closest friend and rival. He would likely go into a state of deep mourning at first. He might isolate himself for a while, just trying to come to terms with the loss.