Naruto may be forced to fight in battles or do tasks that he doesn't want to do. His skills and powers could be misused by Rias for her own purposes. Also, his relationships with his friends in his own world might be affected as he is enslaved in another world. He may not be able to return to his home or communicate with his friends, which could cause a lot of emotional distress for him.
One possible plot development could be Naruto initially fighting against the enslavement. He might use his ninja skills and chakra to resist the control of Rias Peerage. However, as the story progresses, he could start to understand their motives and form an unlikely alliance. For example, they might be trying to protect a greater good that Naruto didn't initially see.
Naruto would likely be deeply hurt. He is a character who values friendship and loyalty highly. Being betrayed by someone he might have considered an ally like Rias would be a huge blow to his emotional state.
Naruto would likely become very distrustful. After being betrayed by Rias, he would find it hard to trust anyone else in the Highschool DxD world. This could isolate him and make his journey much more difficult as he would be on his own without allies.
Well, it could be due to some powerful magic or trickery by Rias. Maybe she has some ulterior motives and uses her special abilities to enslave Naruto. But this is just speculation as it depends on how the fanfiction writer has crafted the story.
Naruto might become more determined. He's the type who turns negative things into positive motivation. So, Sakura's meanness could make him strive harder to prove himself.
One consequence could be that he might face more discrimination from the village elders. In the original story, as Naruto advanced in rank, he gained more respect. But as a genin here, he could still be seen as a troublemaker. Another consequence is that his training might be different. He might focus more on basic genin - level skills, which could make him even stronger in the long run as he masters them to a higher degree.
He might start to compare the fanfiction world too much with the real Naruto story, which could lead to some confusion. For example, if a fanfiction has a completely different view of a character's personality, he may struggle to separate it from the original.
She might spend a lot of time reading and writing fanfiction, which could lead to less time for other activities like socializing or doing school/work - related tasks.
One consequence could be that Naruto has some new powers or abilities. Since the Shinigami is a very powerful and mysterious being, its intervention might leave a mark on Naruto in the form of newfound powers.
Naruto would likely be very angry at first. He is a free - spirited person who values his freedom greatly. So being enslaved would go against everything he stands for. He'd probably try to break free immediately, using his brute strength and any ninja techniques he can muster.