There could be a scenario where a false rumor spreads. The rumor makes Sakura think Ino has betrayed the village or their friendship. Sakura, being impulsive, decides to take matters into her own hands and attacks Ino. Naruto, who always believes in the truth and his friends, investigates and realizes Ino is innocent. He then stops Sakura from harming Ino. Or, in a different setting, if there's a limited resource in the village like a rare herb for medical ninjutsu and both Ino and Sakura need it. Sakura tries to take it from Ino by force, and Naruto steps in to protect Ino.
One scenario could be a competition gone wrong. For instance, if there's a ninja skills competition between Ino and Sakura and Sakura cheats or loses her temper when losing to Ino. She might then try to attack Ino, and Naruto would save Ino. Another could be a love triangle - related situation. If Sakura thinks Ino is stealing Naruto's attention, she could lash out at Ino, only for Naruto to intervene.
In some fanfictions, Naruto might team up with other unexpected characters. Say, he teams up with some of the Akatsuki members who have a vendetta against Pein for some reason. Together, they are able to save Jiraiya from Pein's clutches.
In some fanfictions, Naruto might save Ino from Sakura if there's a situation where Sakura is, say, being overly aggressive or misdirected in her actions. For example, if Sakura accidentally uses a jutsu that endangers Ino during a training session, Naruto could use his quick reflexes and his own jutsu to block the attack and save Ino. Another possibility could be in a more complex plot where Sakura is under some sort of mind - control and Naruto has to step in to protect Ino from her.
One scenario could be that the bullies are picking on Sakura at the ninja academy. Naruto arrives late and sees what's going on. He immediately challenges the bullies to a sparring match, which they can't refuse because of Naruto's status as a top student. During the match, Naruto easily outmaneuvers them and makes them look foolish, causing them to run away in embarrassment.
One common scenario is that Naruto witnesses the bullies taunting Sakura about her looks or skills. He steps in immediately, using his physical strength to stand between Sakura and the bullies.
One scenario could be that Draco witnesses Hermione being bullied by some Death Eater - sympathizing students. He steps in and uses his quick wit and knowledge of magic to outsmart them. Another could be in a situation where Hermione is being wrongly accused of a crime and is facing abuse in the form of unjust imprisonment. Draco, having some influence in the Ministry due to his family, intervenes and clears her name.
One possible scenario is that Naruto senses Sakura is in trouble through his ninja instincts. He quickly rushes to the scene and uses his brute strength to fend off the bullies. Just like how he fought against stronger opponents in the original series, he wouldn't hesitate to protect Sakura.
Sakura's main strength is her physical power. Thanks to Tsunade's training, she has incredible strength that can shatter the ground. She also has medical ninjutsu skills, which can be useful in both saving lives and in combat. For example, she can heal her own wounds or use chakra - enhanced punches. Ino, in contrast, is strong in mind - control techniques. She can enter someone's mind and manipulate them. This is a very unique ability in the Naruto universe.
Maybe in the fanfiction, the situation is more complex. Hinata is being held hostage by the Cloud in a heavily guarded location. Naruto infiltrates the place secretly. He uses his transformation jutsu to disguise himself as a Cloud ninja at first to get closer. Then, he reveals himself and uses his Sage Mode to take on all the guards. He finally rescues Hinata and they escape together.
One popular theme is alternative universes where the characters have different abilities or roles. For example, a fanfiction might have Naruto as a powerful wizard in a magical world instead of a ninja. Another theme is exploring the backstories of minor characters like Tenten or Rock Lee in more detail. Also, there are fanfictions that focus on the rebuilding of the ninja world after the great battles, showing how the characters contribute to the new era.
Simple. Naruto is a hero at heart. He can't stand seeing anyone being hurt, especially his friends. Ino is his friend, so he has to save her from Sasuke.