I've only really seen it in two contexts. Mainly "don't scare the normies", which was largely the advice given to my larp communities to not freak out people in real life with their hobby stuff, and probably also applies to subcultures like furries and such. And secondarily as self-deprecating. I'm a Facebook meme group "Normie Has-Beens" tied to the page "Stale Memes for Normie Has-Beens", and it's certainly not people who consider themselves normal.