Midoriya is better known outside the fandom, and even by some inside of the fandom, as "the protagonist that cries a lot". While he did start the series crying often comically, by around the Internship Arc he had mostly dropped that habit outside of situations in which anybody would cry like the death of one of his mentors or a heartfelt conversation with his mother and these are sometimes gags. Calling him a bad protagonist because he cries a lot has since started to become a Fandom-Enraging Misconception.
On that note, the fandom also tends to make jokes about Midoriya's tendency to break his bones whenever he used his acquired Quirk, One for All. Along with all of his corresponding hospital/infirmary visits. Regardless of the fact that his control over his Quirk's overwhelming power has improved massively to a point that the aforementioned visits have certainly diminished ever since season 3. Various versus communities tease him to no end, immediately assuming he loses most if not all fights including him. They correctly predicted his loss to Asta in DEATH BATTLE!.
Some fans still haven't forgiven All Might for telling Izuku that he couldn't be a hero without a quirk, despite it happening in the first chapter and him regretting it and realizing the error of his ways.
No matter how you view Death Arms as a character, he'll always be remembered as the guy who yelled at Midoriya for trying to save Bakugo from the Sludge Villain.
Mineta's perverted antics have crossed so far over the line at times that a good amount of fans find his actions to be completely unforgivable, even if he's done something heroic since then. His declaration of Jail Bait Wait to a 6-year-old was the last straw for a lot of people.
Todoroki's mistaken belief that Midoriya is All Might's secret love child was never let go. Fancomics and fan art have Todoroki comment◊ about it constantly whenever Midoriya and All Might are together even though it's never brought up again in the manga. It sometimes gets extrapolated into Todoroki believing that Mirio is also All Might's secret love child and that Shinso is Aizawa's illegitimate son. Fanfics sometimes exaggerate this trait to portray him as a conspiracy theorist, constantly coming up with ridiculous theories.
The first thing mentioned about Rei Todoroki is the fact that she was the one who caused Shoto's scar by pouring boiling water on his face. While this happened during a moment of temporary insanity caused by the stress of being in an abusive relationship with Endeavor, Shoto quickly forgave her, and it's later revealed that she had tried to protect Shoto from Endeavor, and later helped give him the epiphany that he doesn't have to be like his father (remembering this helps Shoto use his fire against Midoriya), some fans have never forgiven her for this.
Endeavor's abuse towards his family, notably Shoto and Rei, makes it hard for some fans to forgive him for what he did. The fact that the series extensively doubles down on repeatedly explaining and showing it doesn't help, nor does the immense focus on his Redemption Quest character arc amidst the revelation that Dabi is his thought-dead oldest son, Toya, while showing that Endeavor could only outwardly show that he cared about his Hero legacy, and all but suddenly abandoned Toya for not being able to fill that role like Shoto could in a really misplaced attempt to Give Him a Normal Life. Once this last part was shown, it actually caused many of those who already reviled Endeavor to double down rather than redeem him.
A small but notable portion of fans still holds Tsuyu's claim that breaking the rules to go rescue Bakugo would make Kirishima and the others no better than villains against her. This is despite the fact that Tsuyu soon apologized for saying this, and Aizawa considered Tsuyu as much of an Accomplice by Inaction to the unauthorized rescue attempt as everyone else besides Jiro, Hagakure, and Bakugo.
Toya describing the women of the Todoroki household as useless. Even though he was a kid when he said this and there is no indication he still has this attitude as Dabi despite his many significant vices, this has led to multiple fan works (sometimes jokingly, sometimes seriously) portraying him as a virulent misogynist with a Stay in the Kitchen mindset, which may extend into being a Politically Incorrect Villain in other areas as well.
and fan art have Todoroki comment
