Fanon is really an assumed opinion of characters' personalities.
People would LIKE to believe that stuff they see in doujins is canon, and some probably do. But it's not. That's because the way ZUN has made the characters very open-ended so it's possible to put almost any personality in them. If you dig hard, you might find their true nature, but most people go that far.
Here's a few deciphered.
Kaguya is not a NEET.(Eirin doesn't let her out). Reisen is not heartbroken moe bunnygirl, she's pretty normal. Eirin is actually a really scary person. Sakuya isn't lovey-dove for Remilia, it's more discipline toward her. Alice is not yandere nor tsundere, she's actually a pretty cold person. Reimu is Reimu. Mokou is not tsundere at all, and she's irritated with the bout with Kaguya, not pro it.
Some are true though. Like Yuyuko having a BIG appetite.
This is just part of the IN cast, but there's many more. Lots of fanon personalities stray from the canon ones, but are supposedly 'based off' of it. Well, that's what fanon is for, isn't it?