Perhaps Naruto is in a state of deep depression. He has faced so many challenges and losses throughout his life that he has simply given up on talking to others. He may feel that no one truly understands him and that his words would be of no use, so he chooses silence as a form of protection.
It could be related to some kind of curse or jutsu gone wrong. There might be a hidden enemy who cast a spell on Naruto that restricts his ability to communicate. This would be a very interesting plot point as it would force Naruto to find a way to break the curse while also dealing with the isolation.
One possible reason could be a traumatic event. Maybe he witnessed something so horrible that it made him shut himself off from everyone. For example, if he saw his friends in great danger and couldn't save them in time, it might have led to his silence as a form of self - blame.
Perhaps he's under a powerful genjutsu. In the Naruto universe, genjutsu can manipulate a person's perception and behavior. It's possible that an enemy has cast a genjutsu on Naruto that makes him believe that if he talks to anyone, something bad will happen to them, so he chooses to remain silent.
Perhaps Naruto is focused on his own personal growth and training. He might see the yaoi relationships around him as a distraction from his goals of becoming a stronger ninja. He could be thinking that engaging with others involved in yaoi would lead him astray from his path of self - improvement.
In some fanfictions, the author might make fem Naruto not talk to create an air of mystery around her character. By not speaking, she becomes more of an enigma, which can draw readers in. It could also be related to her character development. For example, she may be shy or introverted at the start of the story and gradually learn to open up and speak as she grows and overcomes her insecurities.
One possible reason could be a misunderstanding. Maybe there was some miscommunication in the past that led Naruto to believe his family didn't understand him. For example, if his family had different expectations for his future as a ninja compared to his own dreams.
One reason could be that Naruto has always been more attracted to those who understand his outcast past better. Sakura doesn't really have that kind of connection with him as she comes from a more normal background. So there's a lack of that fundamental understanding between them which hinders any romantic feelings.
One possible reason could be a miscommunication between them. Maybe Anko feels neglected and then strays. Another reason might be that the writer wants to create a more complex and angsty plot.
One possible reason could be that the Kyuubi's power goes out of control completely. Since Naruto has the Kyuubi inside him, if he fails to maintain the balance, the Kyuubi's raw and unrestrained power might end up killing him.
It could also be that the plot of the fanfiction has Naruto in a situation where talking might put him or his loved ones in danger. So, for their safety and his own, he chooses not to talk.
Well, it could be that the fanfiction is set in a very different universe where Naruto has different upbringing or experiences. But this is quite a stretch because Naruto's caring side is so deeply rooted in his story. It might also be that the writer is simply trying to create shock value by presenting such a counter - intuitive view of Naruto. But in general, it's not in line with the essence of Naruto as we know him from the original series, and it might be a bit of a gimmick to make the fanfiction stand out in a sea of more traditional Naruto stories.
One reason is that some fanfiction authors may lack a deep understanding of Naruto's character. They might write things that are completely contrary to his values and personality just for the sake of creating a 'unique' story. For example, Naruto is known for his positive attitude and strong will, but in some fanfictions, he could be depicted as a negative or spineless character.