His friends might react with shock and confusion. They might not understand why he has been hiding this from them, and it could cause a rift in their relationships until he explains the reasons behind it. For example, some friends might feel betrayed that he didn't trust them enough to share this secret.
One possible reason could be that his eyes hold a special power that he doesn't want others to discover easily. For example, it might be a new type of Sharingan or a unique ability related to his Uzumaki heritage that he needs to keep secret to protect himself or those around him.
Naruto might end up feeling extremely lonely. His family has always been an important part of his life. Without their support and presence, he could become depressed or start making even more reckless decisions. Also, if his family tries to search for him, they could get into danger themselves in the process, which would be an unintended consequence of his hiding.
Perhaps he has hidden the full extent of his Sage Mode abilities. He might be able to stay in Sage Mode for a much longer time than he has shown so far, or have some other undisclosed powers within that mode, like the ability to sense enemies from much greater distances.
One consequence could be that his friends might start to suspect him. Since Naruto is usually an open book, hiding something as significant as his eye could make them wonder what he's up to.
One consequence could be that it changes the way his peers view him. If the fanfiction has some unique or unexpected ideas, it might make them see Naruto in a whole new light. Maybe it could even inspire some of them to start writing their own fanfictions. However, there could also be those who are critical and might tease him about it.
A scenario could be that Naruto is in a diplomatic meeting. He covers his eyes to avoid being influenced by any mind - control or genjutsu that might be subtly used by the other parties. This shows his wariness and also his growth in being able to sense and protect himself from such threats in the political arena of the ninja world.
Another reason could be for disguise. Naruto might be in a situation where he needs to hide his identity. By covering his eyes, which are a very recognizable feature of his, he can make it more difficult for others to figure out who he is. This could be especially important if he is in enemy territory or trying to infiltrate a group secretly.
His relationships with his friends might become stronger. Since he can see more clearly with his god eyes, he can better protect them. His friends would trust him more knowing he has this extra power to keep them safe.
In fanfiction, 'Naruto has no life in his eyes' could imply that he has experienced great trauma or loss. Maybe he has witnessed the death of his dear friends or faced a situation that has broken his spirit. For example, if he lost Sasuke permanently, it could lead to such a state where his eyes seem lifeless, as Sasuke is one of the most important people in his life.
One possible consequence could be that his identity is revealed. If he was using the henge for undercover purposes or to hide his true self, then dropping it would expose him. His friends or allies might be shocked if they didn't know his true form. Another consequence could be that his enemies might take advantage of his revealed state and attack him more easily, as they now know exactly who he is.