Madara Uchiha could be an interesting main antagonist in this crossover. Since he already has strong ties to the Sharingan and was a powerful force in the Naruto series. If he somehow got his hands on the Rinne Sharingan's full power, he would be even more formidable. He could use it to manipulate reality or time, making it extremely difficult for Naruto and his friends to stop him.
Well, it depends on the specific fanfiction. There are countless Naruto fanfictions out there. Some authors might decide to give Naruto the Rinne Sharingan to make him even more powerful or to introduce new plot twists. For example, it could be a result of some special training or a mysterious power transfer in the fictional world of the fanfic.
Another plot could involve a crossover between Naruto's world and a character from the Uchiha clan who has the Rinne Sharingan. They could team up to face a common enemy that is threatening both their worlds. Along the way, they would learn from each other's abilities and cultures. For example, Naruto could teach the Uchiha character about the power of friendship and teamwork, while the Uchiha could show Naruto some advanced Sharingan techniques.
It can also change Naruto's relationships. His friends might be in awe or even a bit scared of his new power. Enemies would surely target him more. Also, it could mean new story arcs. For example, he might have to deal with the dark side of the Rinne Sharingan's power, like being tempted by its overwhelming abilities. And he may need to find a way to use it for good without succumbing to its potential negative influences.
A possible fanfiction could be about the origin of the Rinne Sharingan having some connection to the world of RWBY. Maybe there was an ancient civilization in RWBY's past that had a similar power, and through some sort of dimensional rift, it influenced the development of the Rinne Sharingan in Naruto's world. This would involve a lot of world - building and exploration of both universes' histories.
Well, in the 'Naruto awakens the Rinne Sharingan fanfiction', it's possible that Naruto's character arc takes a whole new turn. With the Rinne Sharingan, he might be able to see the chakra flow in a much more detailed and different way. Maybe he could even communicate with the tailed beasts on a deeper level, using the unique abilities of the Rinne Sharingan. This could lead to new forms of cooperation between them and Naruto, which would be really exciting for the story.
Naruto himself is often a common character. Since it's related to the Naruto universe, he might be a part of the story, either as a friend or a rival to the character with the Rinne Sharingan. Sakura could also be a common character, perhaps as one of the members of the harem.
Sasuke is often a popular character in such fanfictions. His natural Sharingan abilities make it interesting to explore how he would interact with the Rinnegan powers. Fans like to write about him achieving new levels of power by combining or evolving his Sharingan in relation to the Rinnegan.
Madara Uchiha is another popular character in Naruto Rinne Sharingan fanfiction. Since he was one of the first characters to be associated with the Rinnegan (a precursor to the Rinne Sharingan in some ways), fans are interested in seeing how his character would be even more powerful or how his motives might change if he had the Rinne Sharingan. There are often stories that revolve around his further rise to power or his redemption with the help of this powerful eye ability.
In some fanfictions, a character from another dimension enters the Naruto world with the Rinne Sharingan. This new character's power throws the balance of the Naruto world off. The story could revolve around Naruto and his friends trying to understand this new power and either make an ally of the character or defeat them to restore peace in their world.