Well, on one hand, it might make Naruto a bit uncomfortable at first. He's used to being independent. However, as time passes, he might start to rely on Sakura's protection in a way. It could also cause some jealousy among other characters who are close to Naruto, but overall, it could bring Naruto and Sakura closer in an unexpected way. For example, Sakura might start to defend Naruto more vocally, which would show Naruto that she really has his back.
In some fanfictions, Sasuke's overprotective behavior makes Sakura feel frustrated. She's a strong ninja in her own right, and Sasuke not allowing her to take risks can make her feel underestimated. For example, when he stops her from going on a dangerous rescue mission alone.
For the new generation of ninja like Boruto and his friends, they might view Sakura's overprotectiveness as strange. Boruto in particular, who has his own views on Naruto, might not understand why Sakura is so over the top in protecting Naruto. This could lead to some misunderstandings between the generations.
On the other hand, her jealousy could also be a driving force for her to improve herself. She might see Naruto's success and instead of just being jealous, use it as motivation to become stronger. This could lead to a more equal relationship in the long run, as she catches up to him in terms of skills and abilities.
They become more united as they face the challenges of parenting together. Their relationship deepens as they share the joys and sorrows of raising a child.
It often changes drastically. Sakura may initially feel hurt and angry. She might start to question all her previous beliefs about Naruto. For example, if Naruto betrays her trust in a battle situation by seemingly siding with the enemy, Sakura's view of him as a reliable friend and teammate would be shattered.
It might also create a rift within their group. If their friends witness Naruto yelling at Sakura, it could cause tension among the whole group. Some might side with Naruto, thinking Sakura deserved it, while others might defend Sakura, leading to a divided group dynamic in the fanfiction.
It might create a rift between them. If Naruto feels that Sakura is always nagging and yelling, he could start to avoid her. In some fanfictions, this could lead to a period of estrangement where they don't work well together as a team. For example, Naruto might choose to go on solo missions instead.
It could strain their friendship. Naruto might start avoiding Sakura, which would make her realize she's done something wrong and try to fix it.
It can create a rift. Sakura might be hurt by Naruto's outburst and start to distance herself from him. This could lead to a period of coldness between them where they don't communicate as much.
His anger could lead to a complete breakdown of their relationship in some fanfictions. Naruto might feel so betrayed or frustrated that he decides he doesn't want to be around Sakura anymore. But in other fanfictions, it could be a turning point for their relationship. Naruto's anger might make Sakura see him in a new light, as someone who has his own boundaries and feelings, and she might start to respect him more, which could improve their relationship.