One reason could be extreme emotional pain. Maybe he witnesses the death of a very close friend or loved one in the fanfiction world. This overwhelming grief could cause such a physical manifestation as crying blood.
It could also be due to some sort of dark magic or curse placed on him. In many fanfictions, Naruto might be the target of a powerful enemy who uses dark arts. If this magic affects his body in a way that disrupts his normal functions, it could lead to crying blood as a sign of the internal struggle.
It could be that Sakura betrays Naruto's trust. For example, if Naruto entrusts Sakura with a very important secret, like something related to his family or his new power he's developing, and Sakura reveals it to their enemies or uses it against Naruto in some way, that would be a huge blow to Naruto and could lead to him crying.
Perhaps in this fanfiction, Naruto is in a situation where he has no other source of sustenance. He could be trapped in a desolate place with no food or water, and the blood becomes a last - resort option for survival. This would be a very dark and extreme take on the character, as it goes against his usual values.
Maybe Naruto discovers some dark secret about Tsunade's past that she has been trying to hide. For example, something related to her lost loved ones. Naruto, in his usual straightforward way, confronts Tsunade about it without realizing how much it would hurt her, and thus makes her cry.
Guilt. For example, if he fails to save someone he cares about. He'll feel responsible and that could lead to him crying.
One reason could be his regret over his past actions. For example, when he distanced himself from his family to pursue his career at the Ministry. He might realize later how wrong he was and cry out of remorse.
One reason could be the loss of his father. In the Naruto universe, Kakashi had a complex relationship with his father's death. If a fanfiction delves deeper into his younger years, this could be a very emotional trigger for him to cry.
The threat to his friends. James is very loyal to his friends, like Sirius, Remus, and Peter. If they were in danger or if something bad happened to them, it would be understandable for him to cry. For example, if one of them got seriously injured or was in a life - threatening situation, his emotions would be on full display.
In fanfiction, Naruto might be crying because he has reached a breaking point in his journey. He has faced so many challenges, and Minato's appearance and his embrace make Naruto realize how much he has missed having a father. It could also be that Naruto is crying out of sheer happiness to finally be in his father's arms, even if it's in a somewhat surreal or spiritual way.
Maybe he was poisoned. There are many villains in the Naruto world who use poison. If Naruto was poisoned during a fight or an ambush, it could lead to him coughing blood as his body tries to fight off the toxins. Just like how Sasuke was once poisoned and had to be treated.
It could be that Erza scolds Natsu too harshly for something he did wrong. Natsu, who might be more sensitive than he seems, could end up crying from the severity of her words.