Well, there are several reasons. Dumbledore is this all - knowing figure in the original series, but in fanfiction, his actions can be seen as manipulative. He might be making decisions for Harry without really considering Harry's feelings or wishes. Also, Dumbledore's grand schemes might not always be in Harry's best interest. Harry might realize this and get fed up. For instance, if Dumbledore is using Harry as a pawn in a bigger battle against Voldemort, Harry would likely be angry when he figures it out. And Dumbledore's failure to prevent certain tragedies, like the death of Sirius, could also be a reason for Harry's disillusionment.
Maybe he's fed up because the fanfiction often misrepresents the Order's values or actions. In some fanfictions, the Order might be depicted in a way that doesn't align with how he knows them, which could be frustrating.
One popular 'Harry Potter Fed Up with Dumbledore' fanfiction could be 'The Breaking Point'. In this fic, Harry starts to see Dumbledore's manipulative side and decides to take matters into his own hands. Another one might be 'Beyond the Headmaster's Shadow' where Harry rebels against Dumbledore's control. There's also 'A Different Path' which explores Harry's journey when he loses faith in Dumbledore.
One reason could be the over - saturation of certain types of fanfiction. If there are a ton of fanfictions that follow the same tired tropes, like Harry always being the hero in the exact same way or his relationships being portrayed in a very clichéd manner, it could lead to this feeling of being fed up.
Authors might write it because they feel that the original series left some aspects unexplored. They are fed up with the gaps in the story and want to fill them in. For example, the daily lives of the side characters that we didn't get to see much of in the books.
Another reason could be that the fanfiction is full of clichés when it comes to their relationship. It always follows the same tired plotlines, and Hermione, being the intelligent and forward - thinking witch she is, is tired of seeing such unoriginal takes on their relationship.
Some people might write it to explore a darker, more alternative take on the characters. They could be interested in seeing how the story would change if Dumbledore had a more sinister side. It's a way to break the established perception of the characters.
It could mean that Harry Potter (the character in the story) is tired of or annoyed by fan - made fictional stories about him. Maybe he's fed up with how some fanfictions misinterpret his character or put him in situations he wouldn't want to be in.
Perhaps Dumbledore is shown to have a secret alliance with Voldemort in the fanfiction. Harry stumbles upon evidence of this and is filled with rage and hatred. Or maybe Dumbledore had been manipulating Harry's emotions and actions from the very beginning to fit his own plans for the wizarding world, and once Harry realizes this, his hatred for Dumbledore grows. It could also be that Dumbledore has been hiding a powerful magical artifact that could have saved many lives but didn't, and Harry blames him for it.
Dumbledore might underestimate it because he's used to the 'official' version of the wizarding world. Fanfiction can be full of wild ideas that don't fit his traditional view.
In some fanfictions, Dumbledore might bow out of respect for a powerful magical entity or a person with extraordinary abilities. It could also be a sign of his humility in the face of a situation where he realizes he is not the most knowledgeable or powerful.