Dumbledore, even if he's not physically present in the same way, his influence could still be felt. Maybe through memories or pre - arranged instructions. There could be other members of the Order as well, like McGonagall, who would try to stop Harry from ignoring the Order out of a sense of duty and protection.
All Might would probably be one of the first to try to stop Bakugou. As Izuku's mentor and a symbol of justice in the story, he wouldn't tolerate such violence. Another could be their teacher, Aizawa. He's strict and protective of his students, so he'd surely step in.
In this kind of fanfiction, Harry might face various consequences. He could end up in dangerous situations all alone without the support and guidance of the Order. Maybe he stumbles upon a powerful dark magic artifact while on his own and has to figure out how to deal with it without the proper knowledge from the Order.
His closest friends like Ron and Hermione would probably be the most affected. They are used to having Harry around and relying on him. His sudden ignoring would leave them confused and worried.
Sakura might try to stop Naruto. She is one of his closest friends. She cares about him deeply and would be worried about his safety. Also, she would understand that running away is not the best solution to whatever problems he is facing.
He might meet American wizards who are very different from his British friends. Maybe some tough - talking Aurors who have their own way of dealing with dark magic.
Maybe the author wants to explore different relationship dynamics. By having Harry ignore his friends, it creates tension and conflict which can make for an interesting story. It could also be a way to show how fragile their friendship is in certain situations.
Mrs. Weasley could get a bit angry too. She has a temper, and if she feels that Harry is being disrespectful by ignoring her, she might scold him a bit. However, her anger would come from a place of love and concern. She just wants Harry to be okay and part of the family, and his ignoring her goes against that.
He could meet other fans of the same fictional universe. In some fanfictions, gay clubs are places where fans gather to discuss their favorite characters and storylines. So Harry might run into people who are also fans of his world.
He might meet his parents. Since they have passed away, the other side of the veil could be a place where they exist in some form.
There's a chance he'll meet other outcast wizards. These wizards might have been shunned by the wizarding world above ground. They could be very different from the wizards Harry is familiar with, perhaps having their own unique styles of magic. They might initially be hostile to Harry, seeing him as an outsider from the 'normal' wizarding world, but later they could become his allies. They might also know secrets about the underground world that could help Harry in his future battles or quests.