The Hutts would likely oppose Anakin. They have long held power on Tatooine through illegal and immoral means, and Anakin's takeover would threaten their control over the planet's criminal underworld and trade routes.
Some of the local crime lords who have their own fiefdoms on Tatooine would be against Anakin. They would see his arrival and takeover as a threat to their way of life and their ill - gotten gains. Also, there might be those who are loyal to the existing power structures out of fear or self - interest and would resist any change Anakin tries to bring.
There could be elements within the Tatooine government, if there is such a thing in the fanfiction, that oppose Anakin. They might be corrupt and in the pockets of the Hutts or other powerful entities. Additionally, any outside forces that have a vested interest in keeping Tatooine in a state of chaos for their own purposes, like certain smugglers or pirates, would not want Anakin to take over.
Well, perhaps Anakin would start by reforming the podracing scene. Since he was once a podracer himself, he could make it safer and more fair. He might also train a new generation of pilots. And he could use his influence to improve the living conditions of the slaves on Tatooine, maybe even free them all. This would completely change the social structure of the planet.
His mother, Shmi, would definitely be a main character. She could play an even more important role in Anakin's life, guiding him in using his abilities for the good of Tatooine. Also, Watto, the junk dealer, could be a significant character. Their relationship might evolve from one of slave - owner and slave to something more complex, like a grudging friendship or a business partnership as Anakin grows older and more skilled.
Obviously, Anakin would be the main character. His mother, Shmi, would also play a significant role. There could be his friends from the pod - racing days like Kitster. And perhaps some Tusken Raiders who might have a different relationship with Anakin since he stays on Tatooine. Maybe they would see him as a more permanent threat or, in an interesting turn, a potential ally in some local matters.
In this fanfic, Anakin could stay on Tatooine because he has a premonition of the dark side that awaits him if he leaves. So, he decides to stay and focus on bettering his home planet. He might use his natural piloting skills to start a small trading business, using his pod - racer as a start - up vehicle. This would keep him occupied and away from the events that lead him to the dark side in the original story.
Anakin could be angry. He might see his other self as a threat, especially if one represents his dark side and the other his light side. There could be a power struggle between the two versions of himself as they try to assert dominance over the other. Or he could be curious and eager to learn from his other self, about what he could have been or what he can still become.
In the 'anakin never left tatooine fanfic', it could be that Anakin, staying on Tatooine, discovers ancient Force secrets hidden on the planet. These secrets could be related to an old Jedi or Sith presence long forgotten. He might use this knowledge to better the lives of the people on Tatooine. For example, he could use these newfound powers to improve the farming techniques or build better shelters. His story would be one of a local hero, using the Force for the good of his home planet rather than for galactic domination or the fight between the Jedi and Sith.
In this fanfiction, Anakin could interact with the spirit of Yoda. Yoda has a connection to both Anakin and the events in 'The Last Jedi'. Their exchange could be really interesting as Yoda has his own wisdom to impart and Anakin has his own experiences. Also, Anakin might interact with Leia. He knew her well in his own time, and in 'The Last Jedi' she is still an important figure. He could be proud of her leadership in the Resistance or have some concerns about the path she's leading her people on.
The traditionalist elders might oppose Naruto. They are used to the old ways of running Konoha and may see Naruto's takeover as a threat to their power and influence.
He could interact with Luke Skywalker. Imagine Anakin finally getting to meet his son as an ally in the Rebellion. They could train together and share their knowledge of the Force.
Anakin could encounter future versions of his friends or enemies from the past. For instance, he could run into a future version of Obi - Wan Kenobi who has also somehow traveled to that future time. Or perhaps he meets a new generation of Sith who have different motives and methods compared to the Sith he knew in his own time. They could challenge his understanding of the dark side and the Force in general.