One possible reason could be Sakura's constant pining for Sasuke. Naruto might feel frustrated that she's so focused on Sasuke when he's right there for her. In the Naruto universe, Naruto has always been a bit jealous of Sakura's love for Sasuke, and in fanfiction, this could be amplified to the point where he yells at her out of pent - up emotions.
One possible reason could be that Sasuke is frustrated with Sakura constantly trying to get close to him when he's focused on his revenge. He might yell at her to keep her away and not interfere with his plans.
However, in the long run, this yelling incident could be a turning point. If they both later reflect on it, they might come to a better understanding of each other. Sakura might learn to approach Sasuke in a different way, and Sasuke might start to value Sakura's opinions more. So overall, it has the potential to significantly change the dynamic of their relationship in the fanfiction.
Another reaction could be that Sakura becomes more determined. His yelling could fuel her desire to prove herself to Sasuke, whether it's in terms of her strength, her loyalty, or her understanding of him. So instead of being deterred, she uses it as motivation to grow and change in the eyes of Sasuke.
It could also be because of Naruto's own insecurities. He might be afraid that Hinata's actions are drawing too much unwanted attention or putting herself in harm's way, and he yells to try and protect her in his own, brash way. He doesn't want to lose her, but doesn't know how to express it other than through yelling.
Hinata might be very hurt. She's a sensitive person, so Naruto yelling at her could make her feel small and sad. She might start to doubt herself and her abilities.
In many Sakura Naruto fanfics, Sakura is often depicted as a strong - willed character. She uses her medical skills not only for healing but also for strategic purposes during battles.
Mrs Black could be so offended that she starts to plot against Hermione. For example, she might try to get Hermione into trouble with the Hogwarts authorities by spreading false rumors about her.
Harry might become more determined to prove Snape wrong. He's a stubborn character, and Snape's yelling could fuel his desire to show that he's not the misbehaving student Snape seems to think he is.
On Naruto's side, he would probably feel guilty after realizing what he had done. This guilt could make him try to make amends, but Sakura's initial reaction of anger and hurt would still be a big obstacle in their relationship. Their interactions would be filled with tension and awkwardness.