Well, Vegeta would be a likely character. He might be initially suspicious of the female Goku. Maybe he thinks she's a threat or just can't believe there's another Goku - like being. He could be there to add some comical moments as he tries to understand the situation.
In general, it's a bit of a toss-up. The strength of Manga Goku and Anime Goku can vary depending on the specific arcs and battles. Sometimes, it might seem like one is stronger in a particular situation, but that could change in another.
Well, it could be that Goku somehow ends up in the Naruto universe and has a son with a female character there. And this son has both the powers of a Saiyan like super strength and the ability to use chakra for jutsus. Maybe he's an outcast at first because of his strange powers but then becomes a hero.
The theme of femininity in the context of a powerful warrior like Goku is also quite common. Some fanfictions might explore how a female Goku balances her strength with traditional feminine qualities or how she defies the expectations of what a female Saiyan should be like. Also, there could be themes related to love and romance, especially in relation to characters she has a connection with in the original series, but with a new twist due to her being female.
Another possible main character could be the villain that forces the two Gokus to meet. This villain could be a new, super - powerful threat that the two Gokus need to deal with. Their meeting becomes a crucial part of the story to defeat this powerful foe.
Miscommunication can also be a reason. If Chichi misunderstands Goku's intentions, like when he brings home a strange new power - up item that she thinks is dangerous for the family, and she scolds him without really listening to his explanation. Goku, who is not used to having to explain himself in detail, might snap in frustration.
In some fanfictions, Vegeta could be under the influence of some external force. Maybe an evil entity has convinced Vegeta that kidnapping Goku is the key to achieving ultimate power. Vegeta, being power - hungry as he is, falls for it and kidnaps Goku. But later, he realizes his mistake and has to make amends, which can lead to an interesting story arc of redemption and friendship building between the two Saiyans.
There could also be other characters from the Dragon Ball universe making an appearance. For example, Vegeta might show up. He could be curious about Fem Goku and how she compares to Goku in terms of power. Or Bulma could be there, perhaps she's interested in the technology or biology behind Fem Goku's existence.