He might be initially shocked. Since he sees himself as a good mentor, hearing such a harsh accusation from Naruto could leave him speechless for a moment.
He might be really hurt. Naruto has always been an outcast and being called a demon again could reopen old wounds. So he could just stand there in shock and disbelief, his eyes wide with pain.
Neji might get angry. He's a proud character, and being called a girl in a somewhat derogatory way (if that's how he takes it) could make him lash out at Naruto. He could give Naruto a cold stare and tell him to watch his words.
He could also get angry. After all, being misjudged like that is unfair. His anger could lead him to either lash out verbally at Sakura or he could leave the village in a fit of rage, feeling that he is not accepted even by his friends. This could then lead to a series of events where Naruto has to find his own way and Sakura realizes her mistake later on.
One possible reason could be Kakashi's strict teaching methods while not always following his own advice. For example, he might tell Naruto to always be on time for training but be late himself sometimes.
Peter could also be a bit annoyed if it's not a good time. For example, if he was really focused on a test or a lesson he was interested in. But still, he'd probably answer because he knows Natasha wouldn't call without a good reason. He might give her a look that says 'this better be important' while trying to listen to what she has to say.
Percy could also be hurt and go into a silent mode. He might start to question himself, wondering if Annabeth is right. He would then retreat into his thoughts, trying to figure out if his actions really did seem cowardly. This could lead to some internal conflict and self - discovery for Percy.
Naruto could also feel a sense of confusion. He might wonder what he did wrong or what made Fem Kyuubi choose Sasuke over him. This confusion could lead him to question his own worth and his relationships with others. However, in true Naruto fashion, he would eventually rise above these negative feelings and focus on his goals, like protecting the village and his friends.
Sasuke might be initially shocked. He's always been in a sort of competitive relationship with Naruto. But then he might see it as a sign of Naruto's growth and need for family. Sakura would probably be really happy for Naruto. She knows how much Naruto has yearned for a family, and she would see Kakashi as a great father figure for Naruto. As for the older generation like Tsunade, she might be a bit hesitant at first, but then she would support it, seeing that it gives Naruto more stability.
He probably gets very worried. Kakashi is Naruto's teacher and mentor, so he'd likely be immediately concerned and rush to Naruto's side to assess the situation.
Kakashi might immediately offer a comforting presence. He could put his hand on Naruto's shoulder and just be there silently, letting Naruto know he's not alone.