A powerful dark sorcerer could be the main antagonist. He senses the unique connection between Naruto and Shizune and wants to use it for his own evil purposes. He might try to corrupt Naruto or use Shizune's medical knowledge against the village. Naruto and Shizune would have to fight together, relying on their family bond to defeat this powerful foe.
It could be a rogue ninja who has a vendetta against Shizune's family. This ninja might see Naruto as an obstacle in his path to revenge. He could target Naruto to get to Shizune and try to break their family - like bond.
It could be a rogue medical ninja who was once a colleague of Shizune but turned to the dark side. This antagonist might be jealous of Shizune's position in the village and her relationship with Tsunade. He or she could try to undermine Shizune's new discovery or training program in the fanfic by causing chaos in the village and framing her for it.
There could be a group of villagers who are superstitious. They believe that Shizune's presence in the hospital during a recent epidemic is what made it worse (even though it's completely untrue). Naruto has to comfort Shizune and then he tries to educate the villagers about the real causes of the epidemic and how Shizune was actually helping.
Perhaps an old enemy of Naruto's who resurfaces and decides to target his family. This could be someone who was defeated by Naruto long ago but has now grown stronger and wants to cause harm to his loved ones. They might also see Kakashi as a threat in protecting the family.
It could be a relative from his family who was behind the abandonment. Maybe they want to keep Naruto away from some family secret or power, and they will do anything to stop him from finding out the truth.
Maybe it's an evil organization that wants to isolate Naruto. By making his family forget him, they hope to break Naruto's spirit and prevent him from becoming a powerful force in the ninja world. So they target his family's memories as a way to get to him.
It could be a family member who has a personal vendetta against Naruto and is the main instigator of his being shunned. Maybe an older cousin who is jealous of Naruto's potential.
It could be a rogue ninja who has a vendetta against Naruto and wants to target his family. Maybe this ninja was once defeated by Naruto and now wants to take revenge by harming his loved ones, especially his and Sakura's child.
It could be a powerful ninja from another village who sees Naruto's godlike powers as a threat to his own plans of domination. Since Naruto is already feeling vulnerable due to his family leaving him, this antagonist might try to take advantage of his emotional state.
One idea could be that Naruto and Shizune discover they are long - lost relatives. Maybe there was some sort of hidden family secret. Naruto could then learn a lot about his family's past from Shizune, and they could bond over that. Shizune could also teach Naruto some unique medical ninjutsu skills that were passed down in their family.
It could be someone from the Naruto universe who doesn't like Naruto's newfound fascination with Aku. For example, Danzo might see Naruto's interest in Aku as a threat to the stability of the village and try to stop Naruto from further exploring Aku - related things. So, Danzo could be the main antagonist in this case.