It's possible that his father is not what Anakin expected. He could be from a different planet or species. Their meeting might cause Anakin to question his own identity. He may struggle with whether to accept his father or reject him due to the differences. And this internal conflict could be a major plot point in the fanfiction, affecting Anakin's decisions and actions in the story.
In some fanfictions, when Anakin meets his father, it could be a very emotional moment. His father might reveal secrets about their family or Anakin's true origin. It could also lead to Anakin getting some long - sought - after guidance or a new sense of purpose.
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.
There is no such appropriate fanfiction. In the Star Wars universe, which Anakin belongs to, there are certain values and moral codes. This kind of plot would completely shatter the integrity of the story and the characters, and it's not something that the fan community or the general public would tolerate.
Goku's reaction could be a mix of shock and happiness. On one hand, he never expected to actually meet his parents. On the other hand, he has always longed for a family connection. He might start asking them a million questions right away about their lives, Saiyan culture, and what it was like when he was born.
One possible scenario could be that Blu is initially nervous when he meets his mother. He might be hesitant, but as they start to interact, he realizes how much he has in common with her. For example, they could both have a unique way of communicating with other birds. Their reunion could be filled with a mix of emotions, from joy to a bit of awkwardness at first.
She could be a former pirate captain herself. Maybe she was one of the most feared pirates in her time, and her skills and reputation were passed down to Luffy in some way, even if he didn't know it was from his mother.
His friends from the guild could be important. For example, Happy might be there to share in the joy of Natsu meeting his mother. Happy could also provide some comical relief during the emotional encounter.
There could be a power - hungry being who wants to use Goku's mother for their own gain. When Goku tries to meet her, this being tries to stop him because they know that if Goku and his mother reunite, they will be able to oppose their evil plans together.