One possible consequence is that it could change the dynamics of his battles. He could easily surprise his enemies and gain an upper hand in combat. For example, he could sneak up on opponents and land a powerful attack without them even realizing he was there.
Another consequence might be in his relationships. His friends could become suspicious of him if he uses his invisibility in a way that seems sneaky. Also, it could lead to some comical situations, like when he accidentally scares his friends while invisible. Moreover, it could also affect how he is perceived in the ninja world. Some might see him as a greater threat and others might try to figure out how to replicate his ability.
One consequence could be that he becomes more curious and starts to explore places he shouldn't. Since he can be invisible, he might sneak into the restricted section of the library or into the teachers' lounge to uncover secrets. This could lead to him getting into trouble or finding out important information that changes the course of the story.
One possible reason could be some sort of ancient bloodline connection. Maybe there was a long - forgotten ancestor who had a pact with the fox spirits, and that power has been dormant in Naruto's bloodline until it gets activated somehow. Another reason might be due to a powerful jutsu that was cast on him as a baby, a jutsu that was meant to protect him but also had the side effect of giving him the ability to turn into a fox.
The fact that Naruto can't read or write fanfiction doesn't have any practical consequences in his own universe. His story is about his journey as a ninja, his growth in power, his friendships, and his fight against evil. Fanfiction is an outside concept that doesn't play a role in his story. He doesn't need this ability to succeed in his own world of ninja battles, village politics, and personal development.
Speed. Wolves are known for their speed, and Naruto in wolf form could move much faster than in his normal human form. This would be a great advantage in chasing enemies or getting to a location quickly.
He might also face moral dilemmas. For instance, using this power to heal someone might seem noble, but if he uses it to harm or manipulate others, it would be a different story. He has to constantly struggle with the right way to use this power.
Well, it could be due to a bloodline limit that was previously unknown. Naruto might have some distant ancestor with the ability to transform into a wolf, and through some circumstances, this latent ability surfaces. Or perhaps he made a deal with a powerful wolf - spirit in a mysterious forest, and as part of the deal, he gained the ability to turn into a wolf.
Naruto could use his invisibility for stealthy missions more effectively. He could gather intelligence without being detected, which would give Konoha an edge in battles or political situations. However, it could also make him a target for those who know about his new ability and want to capture or study it for their own purposes.
In some fanfictions, Naruto might turn invisible through a special jutsu he discovers or is taught. It could be a new form of ninjutsu that manipulates light and reflection to make his body unseen, much like the way some real - world concepts of invisibility work by bending light around an object.
Naruto may be forced to fight in battles or do tasks that he doesn't want to do. His skills and powers could be misused by Rias for her own purposes. Also, his relationships with his friends in his own world might be affected as he is enslaved in another world. He may not be able to return to his home or communicate with his friends, which could cause a lot of emotional distress for him.
Naruto might become more determined. He's the type who turns negative things into positive motivation. So, Sakura's meanness could make him strive harder to prove himself.