Well, Kakashi might use his Sharingan to intimidate the civilians and create an opening to grab Naruto. His quick jutsu skills could also be a factor, like using a clone to distract the civilians while he gets Naruto to safety.
Kakashi is a very experienced ninja. He might start by trying to reason with the civilians in a calm yet firm voice. However, if that doesn't work, he would rely on his combat skills. He could perform some acrobatic maneuvers to reach Naruto. His ability to move swiftly and his knowledge of various escape techniques would surely help him rescue Naruto. For example, he could use his body - flicker technique to suddenly appear next to Naruto and then disappear with him before the civilians could react.
Perhaps the civilians have been influenced by some anti - Naruto propaganda. They might not understand the true nature of Naruto and the fact that he has no intention of harming them. Also, they could be in a state of panic after some events that they wrongly blame on Naruto. For instance, if there was some minor destruction in the village that was actually caused by other factors but they assume it was Naruto's doing because of his connection to the Nine - Tailed Fox. This could lead them to try and harm him until Kakashi steps in to rescue him.
In some fanfictions, it could be due to a special jutsu gone wrong. Maybe a jutsu that Kakashi was using to transfer some of his chakra to Naruto for a mission accidentally transferred his Sharingan power as well.
Naruto could show his 'like Kakashi' traits in his mentoring style in the fanfic. Kakashi is a great mentor to his students, and if Naruto is like him, he might start to take on apprentices and teach them in a patient and knowledgeable way, passing on not just ninja skills but also important life lessons.
Kakashi's parenting style would likely be more laid - back compared to some of the stricter ninja parents. He might give Naruto more freedom to explore his own way of being a ninja. For example, instead of forcing a particular fighting style, he would let Naruto experiment and find what suits him best.
The moment when Kakashi actually reaches Naruto and stops him from harming himself is crucial. He could use his speed and strength to grab Naruto's hands if he was about to use a weapon on himself. Kakashi's presence alone at that moment can be a shock to Naruto, making him pause and re - consider.
Naruto might also try to find alternative ways to gain strength. He could explore the forest around the village to find new training areas or discover new chakra - related phenomena. He has a curious nature, and this could lead him to stumble upon something that gives him an edge in his training, like a hidden hot spring that has special chakra - enhancing properties.
In the fanfic, Naruto could pick up Kakashi's habit of being a bit of a mystery. He might not reveal all his thoughts and plans right away. Also, his sense of humor could change to be more dry and understated, similar to Kakashi's. He may start using more one - liner type of remarks during interactions. Naruto might also show more patience in teaching and guiding others, as Kakashi is often seen doing with his students.
In the original Naruto story, Kakashi is a mentor and a positive influence on Naruto. He teaches him valuable skills and life lessons. But in the fanfic where he abuses Naruto, it completely goes against that positive relationship.
In this fanfiction, Kakashi could help Naruto in his training through mental conditioning as well. Naruto is often impulsive, so Kakashi may work on his patience and decision - making skills. He could use his Sharingan (if applicable in the fanfiction) to analyze Naruto's movements during training and give him detailed feedback. Moreover, Kakashi could introduce Naruto to different types of enemies and battle scenarios in a controlled training environment, which would broaden Naruto's understanding of combat and make him a more versatile ninja.
Well, it could strain their relationship. Avoidance usually creates distance, and in this case, Kakashi might feel hurt or confused as to why Naruto is avoiding him.