They might interact with a mix of caution and boldness. Harry, out of habit, would be cautious not to upset the Dursleys too much. Ginny, though, could be bold. For example, she might directly ask Vernon why he's so against magic when it can do so many wonderful things. Harry would be in the middle, trying to translate the Muggle - magic misunderstandings between them.
In fanfiction, when Harry and Ginny meet the Dursleys, there could be a lot of tension. The Dursleys are not fond of anything related to magic. Ginny, being a confident witch, might stand up to the Dursleys' rudeness towards Harry. Harry, on the other hand, would be in an awkward position as he has to deal with his Muggle family and his magical girlfriend at the same time. There could be some humorous exchanges as Ginny tries to understand the strange Muggle world of the Dursleys while also showing them that magic is not something to be feared.
In such a fanfiction, perhaps Ginny might initially be met with the Dursleys' typical rudeness. They could be shocked by her magical abilities which she might accidentally display. For example, if she gets frustrated with their behavior, a magical item she has might react in an unexpected way.
It could be Ginny. Since she is the one being introduced to the Dursleys, the story might focus on her reactions and how she deals with this rather strange non - magical family.
Ginny would likely be protective. She loves Harry and knows about his difficult past with the Dursleys. So she would probably stand up for him right away, not tolerating any of their mean remarks.
There are many ways it could be written in fanfiction. Ginny might use her knowledge of the wizarding world and Hogwarts' secrets. She could use a special spell that she learned from an old book in the Hogwarts library. This spell could create a portal right inside the Dursleys' living room that only Harry can see. Ginny could then communicate with Harry through a magical device, tell him about the portal, and he can use it to escape from the Dursleys. Ginny would have to be very careful and plan everything precisely to avoid detection by the Ministry of Magic, as using magic around Muggles without permission is strictly prohibited.
Well, they might have a really awkward encounter. Ginny could be shocked by the Dursleys' rudeness towards Harry. And Harry would probably be super tense, trying to keep Ginny from getting too involved in the Dursleys' mean - spirited remarks. Maybe Ginny would stand up for Harry more than he's used to, which could lead to an unexpected turn in the relationship between the Dursleys and Harry.
Some fanfictions might depict that the wizarding community might see her as a hero. However, others could show that she faces backlash from some conservative wizards who think she overstepped her bounds. They might try to isolate her at Hogwarts or spread rumors about her. But her friends like Harry, Ron and Hermione would surely support her through it all.
The author could focus on Ron as well. Since he's Harry's best friend and Ginny's brother, his reactions to their first meeting could be interesting. Maybe he's a bit overprotective of Ginny at first.
If Harry and Ginny meet the Marauders in fanfiction, it would be a moment full of emotions. Harry has always longed to know more about his father, and this would be his chance. The Marauders, on seeing Harry, might see a lot of James in him. Ginny would add a different dynamic to the group. She could be the voice of reason at times. Together, they could create new memories. For example, they might team up to play a prank on Snape's memory or something, which would be both funny and a way to pay homage to the Marauders' legacy.