Sorry for late comment and not OP but HCs stand for headcanons.
say the headcanon is that a character is gay, possibly dating their canonical rival (since that's been a popular pairing since the dawn of online fandom) and they'll all get mad if you ship that character with someone of the opposite sex.
I am familiar with the term, here is what I think it means.
I thought a headcanon is that you take an already established character who has lots of traits and relationships with other characters but the source material doesn't give you every single detail.
I struggle to come up with an example character just now but a headcanon I heard about was actually about Solid Snake from Metal Gear Solid.
In MGS1 there is an optional briefing cutscene you can watch, in it Snake gets to know that the leader of the terrorists, Liquid Snake, looks
exactly like him save for a slightly different skin tone.
This is the only difference that is pointed out between the two of them.
Coincidentally the cutscene where all this is said uses moving detailed stills with a limited colour pallete.
However Solid Snake has brown hair while Liquid Snake is blonde, and since this rather distinct difference isn't explicitly pointed out the headcanon is that Solid Snake might be naturally blonde too and is dying his hair.
I can certainly see him being blonde in this picture. Here is the cutscene if you want to look yourself.
Headcanons, I thought, were fans filling in those empty spaces with their own details as to why the character is the way he is in
canon.
Drongo's example I quoted just now I would classify as simple fanfiction since there is simply no canon material to suggest the rivals would date.
Headcanons should be mainly about a character's past and have enough plausible evidence to make some sort of sense.