I haven't actually read this specific fanfic. But generally, if 'camp camp' meets Max's shitty parents in a fanfic, it could be a really interesting exploration of the characters. It might show how Max's relationship with his parents affects his experiences at camp, and how the camp environment in turn influences his view of his family situation.
One possible theme could be family dysfunction. Since Max has shitty parents, it's likely that the fanfic will explore how a broken family affects a child like Max. Another theme might be the search for acceptance. At camp, Max may be looking for the acceptance he doesn't get at home.
I haven't read this fanfic specifically. But generally, in a 'camp camp meets max's shitty parents' fanfic, it might explore how the camp camp environment and characters interact with Max's difficult family situation. Maybe it shows how the friends at camp support Max when facing his shitty parents, or how Max's experiences at camp change his perspective on his family.
It could be that Max's shitty parents show up at the camp unannounced during a big event. This causes a scene, and Max is embarrassed. But then the other campers and counselors rally around Max. They might put on a show of how great the camp is and how much it has helped Max, in an attempt to make his parents see the value of the place and, by extension, Max's experience there.
It can contribute by expanding the lore. Fans get to see a part of the story that isn't really explored in the original show. It gives more context to Max's character.
One good example could be a fanfic that focuses on Max's relationship with his parents before he came to the camp. It might explore how their parenting style influenced his rebellious nature. For instance, it could show that his parents were overprotective, which made Max act out in order to gain some freedom.
One interesting aspect could be the exploration of Max's family background. It might give insights into why he is the way he is in the 'Camp Camp' series. For example, if his parents are strict or neglectful, it could explain his rebellious nature.
You need to establish the tone. If you want it to be comical, you can have Max's parents be really out - of - touch with the camp life. For example, they think it's a luxury resort. If you want it to be more serious, explore the emotional distance between Max and his parents. Write in a way that shows Max's internal struggle when dealing with his parents, whether it's through his thoughts or his actions.
Character interaction is also a big theme. The different personalities from both shows collide. You might see David from Camp Camp trying to keep everyone positive in the face of Gravity Falls' oddities, while Dipper is trying to figure out how to use Camp Camp resources to help in his mystery - solving. It's really interesting to see how they play off each other.
Another option is to check out some fanfiction communities on Reddit. There are subreddits dedicated to both Camp Camp and Gravity Falls where fans might share or discuss their 'camp camp meets gravityfalls' fanfiction ideas or links to their works.