One reason might be that the fanfiction doesn't capture the essence of Mcgonagall as Harry knows her. He has a deep understanding of her from their time at Hogwarts, and if the fanfiction misses that, he won't like it.
Harry might not like Mcgonagall fanfiction because he doesn't want to see her character manipulated in fictional scenarios that go against what he believes in. He has a certain respect for her, and when fanfictions play around too much with her character in ways he doesn't approve of, he'll dislike it.
One reason could be the alteration of McGonagall's personality. If in fanfiction she is made to be overly strict or mean, Harry, who knows her real character, would dislike this new version. In the original series, McGonagall was strict but fair, and any deviation from that in fanfiction might be off - putting to Harry.
One reason could be that he doesn't like others taking creative liberties with his story. He might feel that it's his story and only the original version should be the 'true' one.
One reason could be the stress of fighting Voldemort. Harry has so much on his shoulders, and McGonagall is a figure of authority and comfort. He might break down in front of her when the pressure becomes too much. For example, when he has to face difficult decisions like whether to sacrifice himself or when he feels responsible for the safety of his friends.
It could also be due to some actions of McGonagall that seemed suspicious to Harry. Perhaps she made a decision regarding Hogwarts or Harry's safety that Harry didn't fully understand at the time. In the complex world of the wizarding school, decisions are often made with many factors in mind, but Harry might not be aware of all of them, leading to his distrust.
One possible reason could be that she is under some sort of dark magic influence. Maybe a spell has been cast on her that makes her act out of character and abandon Harry.
Perhaps he likes to see how fans re - imagine his character. He might be curious about how others view his actions and motives throughout the story.
Maybe in that fanfiction, McGonagall has some actions that Harry misinterprets. For example, she might be too strict with him in a way that he can't understand at that moment.
One reason could be that the fanfiction is set in a different universe where the characters' personalities are slightly altered. So, this 'new' Harry just doesn't click with Ginny in that version. For instance, if the fanfic is a darker take on the story, Harry might be more jaded and not open to a relationship with Ginny.
One reason could be a change in Dumbledore's personality. If he's depicted as being cold or distant in fanfiction, Harry, who knew him as a mentor figure, might not like it.
It could also be that in the fanfiction, McGonagall has shown some form of bias. Maybe she seems to favor certain students or groups over others, and Harry, being the one who always stands up for fairness, starts to distrust her when he notices this behavior. He might feel that she is not as just as he once thought her to be.