It seems that such as that could cause issues with your anonymity if you live in a smaller town, and anonymity is an asset in this business. So no, I would not post such on my social media. Although I am a member of some of the groups, I don't tell a lot of people that I am a mystery shopper. In some situations, I do say that I do a little business reporting along with my other.
How many legs does a dog have if you call the tail a leg?
"Four. Calling a tail a leg doesn't make it a leg."
-- Abraham Lincoln