Oh... oh boy... I have a lot to say about this.
I do think headcanons are really... really... REALLY REALLY REALLY REALLY REALLY annoying. People might think they're harmless and for the most part, sure.
But then you got weirdos shipping brothers with their sisters and protagonists with antagonists. One of the worst ones I continue hearing about are people shipping Johnathan and Dio, raising Giorno but like.... Dio used Johnathan's body WITHOUT his consent to have sex with a neglectful prostitute... the metaphor there was Dio was defiling his legacy. On top of that the two were adopted brothers. Johnathan literally hugged Dio when he was dying because he loved him THAT much and Dio's response throughout 3 behind the scenes was straight up "I respect him, but Imma use his body to screw as many girls as possible. Who cares if I get some of them pregnant? Also oh yeh, I'm bisexual and Johnathan was obviously a vanilla straight traditionalist dude (Araki has pretty much implied in dialogue that he wrote in the games... that're non-canon, but still, he's made this a consistent detail... that he's a little too... unsupportive... of homosexuality lmao), Imma screw guys as well because why not!!! Again with my brother's BODY." But people make that situation to be all cutsey and it's so gross when fans can't read between the lines.
I also hate it when people ship kid characters. And yes... I mean KID characters. I'm not a fan of Loud House or My Hero Academia (well I was briefly a fan there, but... take a guess why I jumped ship) but the discourse there is nothing short but creepy. I'm going to sound a bit uptight here, but I think... maybe once people reach a certain age they should ship characters that're THEIR AGE.
I also have a problem with people assuming character's identities. Especially when they're apart of different cultures and they don't bother to research why they could be offensive. The Encanto fandom showed me what headcanon fandoms can be when they're out of control and I was like "Oh thank GOD that didn't happen with Coco". Like how they tried to assume Bruno as this neurodivergent icon when the dude was superstitious (I'm not Columbian, but I was familiar with all the stuff he was doing, which is why I'm a little more offended with this one) or when they thought that one chick had tics when really that was a mannerism people make in the South when they gossip. Columbians were coming out and calling these people racist.
I also don't like when headcanons eventually lead to claiming a character as another group's officially speaking? Let me tell you what I mean. There was this one TV Show (I swear I wish I can find it, if someone reads this comment please let me know) where this one chick is wearing this black trench coat and she has to disguise herself as a man to fight crime. I found so many people uncomfortable with the fact that new people getting into the show are trying to turn her into a trans person when they're like "Well I mean... why can't she just be a normal woman that happens to be wearing this type of stuff?". Which is another headcanon I hate where they're like "This character HAS to be this, this character HAS to be that" which ends up leaving little representation for people who were attracted to these characters in the first place? People talk about iterations and how they'll always have the original when they get their hands on the series, but what if the new series takes out the core reasons about what made the character so special in the first place and becomes even more popular for the wrong reasons? Velma is an example of this where the series is made by people who wanna make fun of people who just want more Scooby-Doo!.
But the worst head canons are when you come out and change history imo. I remember hearing about this British play regarding Joan of Arc and how they were going to depict her as someone struggling with sexuality and identity and when you get more into it and you see more images you're like "this person is just straight up horny for a HOLY ICON". There's parodies... there's satire... and then there's seeing someone's headcanons come to life.
I can obviously go on about headcanons between streamers, headcanons from sacred stuff... but I feel like this text is going to go on forever.