Some members of Young Justice could be embarrassed. For instance, if there are romantic fanfictions about them that are a bit too cheesy or if their weaknesses are overly emphasized in a not - so - flattering way. But others might be really intrigued and want to explore more of what the fans think about them.
Some of them might be amused. They could find the different takes on their characters and stories quite entertaining. For example, Superman might chuckle at a fanfic that has him in a comical situation.
Naruto would be a bit of a wild card at first. His brash and head - strong nature might clash with some of the more reserved members of the Young Justice team, like Aqualad. But his determination and loyalty would also be something that the team could quickly come to respect. He would probably befriend Superboy quickly as they both have a bit of an outsider feel.
In this type of fanfiction, magic could play a role in character development. For Naruto, experiencing a different type of power system like magic in the Young Justice world could make him question his own ninja way. He might start to adapt some of the magic concepts into his own fighting style. And for the Young Justice characters, learning about Naruto's 'magic' (chakra) could open their eyes to new ways of thinking about power and how to use it more effectively.
The more idealistic members of Young Justice like Robin might be immediately suspicious of Loki. He represents chaos and trickery, which goes against Robin's sense of order and justice. He would probably try to keep the team away from Loki until they know his true motives.
He'd probably be confused at first. Naruto is used to being among friends and comrades. But then, his determination would kick in. He'd likely try to talk to them, to understand why they think he's a threat.
In a Young Justice fanfiction, Naruto's Sage Mode could change the power dynamics significantly. His Sage Mode gives him access to nature energy, which could interact in strange ways with the various powers and technologies in the Young Justice world. For example, his ability to blend into nature while in Sage Mode might make him an excellent spy or infiltrator. Plus, his battle experience and strategic thinking from the Naruto world could help the Young Justice team in their missions.
One possibility could be that Naruto's anti - hero status in the Young Justice fanfic is due to him being a loner. Maybe he doesn't trust the Young Justice team at first because of his past experiences. He might have his own way of doing things that doesn't always align with the team's methods, like being more brutal in combat against villains.