In some fanfictions, Percy's sister might hurt him emotionally by betraying his trust. For example, she could share his secrets with others, making him feel exposed and betrayed.
A common scenario could be over inheritance or family heirlooms. If there's something valuable in the family that both Percy and his sister want, she might scheme to get it all for herself, leaving Percy feeling cheated and hurt.
Maybe she's jealous of Naruto's popularity or his strength. It's possible that she feels overshadowed by him all the time and that jealousy turns into resentment, leading her to hurt Naruto.
Another way is if his sister has some special powers that she can't fully control yet in the fanfiction world. And during a training session or an accidental encounter, her powers lash out and end up hurting Naruto.
Perhaps she's a sister who was thought to be dead but actually survived. She could have been corrupted by the experiences she had while being 'dead'. When she returns, she blames Percy for not saving her properly. This false blame leads her to betray Percy. She could start spreading rumors about Percy being a coward or a bad leader among the demigod community.
It could be an old enemy like Luke. He has always had a vendetta against Percy and would not hesitate to cause him harm. Maybe Luke has some new evil plan and hurting Percy is part of it.
Well, it could be because of jealousy. Maybe his sister gets more attention from their parents or is better at something that Percy wishes he was good at.
The implications are mainly negative. It promotes an unethical and immoral relationship that goes against basic human values. It can also be disturbing for readers who have a normal sense of right and wrong.
This is a rather disturbing concept as incestuous relationships are not acceptable in society. However, there might be some very dark and inappropriate fanfictions out there that explore such themes, but I would not recommend seeking them out as they go against moral and ethical norms.
One reason could be jealousy. If Naruto is getting more attention or has achieved more in the ninja world, his sister might be jealous and this could lead to her actions that hurt Naruto, either by spreading false rumors or directly confronting him in a hurtful way.