I was trading heavily on localbitcoins for years, in person trades and money transfer services and I never had to fill out any KYC forms. Never sent in ID, or any identifying information outside of a phone number that I used to talk to buyers and sellers. Not sure why you feel there was no privacy?
So was I, until several years ago when they transitioned to demanding KYC from all their users as Solosanz has provided links for above. At that point I immediately stopped using them and transitioned to better options. Now I use mostly Bisq, but a handful of other platforms too.