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 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.
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.
They would likely start with some mutual curiosity. Naruto would be intrigued by Rias's devilish appearance and powers, while Rias would be interested in Naruto's ninja abilities. They might exchange stories about their respective worlds, with Naruto talking about his village and his friends, and Rias sharing about the devil society. Interaction could also involve sparring sessions to test each other's strength.
Naruto would probably interact with the other members in a very friendly and enthusiastic way. He's always been the type to make friends easily. He might share his ninja stories with them, and they in turn could share their own experiences in the supernatural world. His positive attitude could brighten up the group and break the ice in any tense situations.
At first, Naruto might be deeply hurt by the rejection. But this could lead him to become more introspective. He may start to question his own actions and motives more. For example, he might wonder if his way of approaching Rias was too brash or if he misread the situation entirely.
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.
In this fanfiction, the plot development might begin with Naruto being transported to Rias' world or vice versa. When Naruto rejects Rias, it causes a stir in the power balance of Rias' world. Her peers might be shocked or angry at Naruto's refusal. Meanwhile, Naruto is just trying to figure out how to get back to his own world. As the story unfolds, Rias might try to use her charm or power to change Naruto's mind, but he remains steadfast. This could lead to conflicts not only between Naruto and Rias but also between Naruto and the other characters in Rias' world who have an interest in the situation. Naruto will have to use his ninja skills and his strong will to navigate through this strange new world while constantly rejecting Rias' attempts to draw him in.
Maybe Naruto has his own set of values and the concepts in Rias fanfiction go against them. He's from a different fictional universe with its own rules and ethics, and the ideas in Rias fanfiction might seem out of place or even wrong to him.
For the Naruto fandom, bashing fanfiction could potentially turn some fans away from the overall fanfiction community if they feel that their beloved character is being unfairly targeted. In the case of Rias and Issei's fandoms from High School DxD, it could create a stir as well. Some fans might engage in debates with the writers of the bashing fanfiction, trying to defend the characters. This can lead to both positive and negative interactions within the fandoms. On one hand, it can spark discussions about the characters' qualities, but on the other, it can also lead to a hostile environment if not handled properly.
Well, it could be due to their different personalities. Naruto is all about hard work and loyalty to his friends in his own universe. Rias Gremory has a more complex and sometimes manipulative personality in her story. In fanfiction, the writer might want to create a conflict by making Naruto dislike her, perhaps because he sees her methods as being at odds with his own values.