That really sucks! Sorry that happened to you.
I can't say I've never mentioned mystery shopping on FB but in general, I try not to mention it on social media or even in real life that much. I don't think that many people outside of my family know I do it. It's not my primary job. I live in a big city, but you never know who you might know. My husband works in sales and a lot of his former co-workers end up in service industry jobs around town so I have just kept it close to the vest.
I even had a really weird coincidence.. I mainly do restaurant shops and since it's not my primary job, I am choosy about where I go and kind of try to just go places I want to try, higher end places, places in the city etc. I was talking to my co-worker one time about how I was going to shop a certain chain Asian restaurant in my suburb (close to where I live but not that close to the city location where we work). This place is thought of as waaaayyyy to "Americanized," at least in my region where there is a ton of good Asian food. I kind of played it up because it's not something I would normally go to and my co-worker is a restaurant snob. But then hubby and I went and we had a good time, great service, great shop, food was not very "authentic" but it was super tasty. Basically my assumptions were wrong, so I came in the next week and we had a whole conversation about that. We work in an open office and anyone could hear us. Then a little while later our office hired a new girl. A few months later my co-worker was chit chatting with her and found out her boyfriend is the MANAGER OF THAT EXACT RESTAURANT!!! LOL!!! So if she had overheard this, I would have really been an a-hole on a couple of levels and I learned my lesson.