One interesting 'Harry is raised by McGonagall' fanfiction could be 'A Different Start'. In it, McGonagall takes on the role of a mother figure very seriously. She teaches Harry about magic in a more traditional and strict way, which makes for a really unique take on his character development.
He'd probably be more disciplined. McGonagall is a strict teacher, so as a guardian she'd likely enforce rules more firmly than the Dursleys or even Dumbledore. Harry would be less likely to break rules on impulse.
Another plotline could involve how McGonagall deals with Harry's fame. Since she's very no - nonsense, she might shield Harry from the public eye more effectively. This could lead to a Harry who is less influenced by the adoration and more focused on his studies and personal growth.
Since McGonagall has a strong sense of justice, Harry would probably have an even more acute sense of right and wrong. He would grow up with her values of fairness and loyalty deeply ingrained. This could lead to him being more proactive in standing up for others who are being wronged, not just because of his own experiences, but because of the values he was taught by McGonagall.
Perhaps when Harry is wrongly accused of something, and McGonagall uses her influence and knowledge to prove his innocence. She stands up for him in front of the whole school or the wizarding authorities, which is a very significant moment of her protecting Harry.
She might use her magic skills to shield Harry from physical harm. For example, she could cast protective spells like a strong shield charm when Harry is in danger from dark wizards. Also, she may use her authority in Hogwarts to keep him away from those who wish to harm him, like making sure he is not alone in dangerous areas of the school.
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.
One common plotline is McGonagall protecting Harry from the Ministry of Magic when they wrongly suspect him of something. For instance, if the Ministry believes Harry is using Dark Magic, McGonagall stands up for him, using her influence and knowledge of Harry's character to prove his innocence.
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 great Harry McGonagall fanfic is 'The Transfigured World'. It shows an interesting alternate universe where McGonagall has to deal with some unique magical challenges. Another is 'McGonagall's Legacy' which delves into her past and how it shapes her role at Hogwarts. And 'Harry and McGonagall's Unlikely Alliance' is also a good one, with a great plot of them teaming up against a common enemy.