I use a nickname Ilikebeans but agreed, the degrees of separation can be vanishingly small.
I'm at an international school, my dc attend it, I'm friendly with other parents & have to be VERY careful about boundaries.
For example I teach my best friend's year 7 dd & another friend's year 10 ds. They both have professional involvement with my dc. We had a lovely boozy weekend away together last week.
Come Parent's Day, we will inevitably be having 'so, Mrs Crow, is my child reaching his/her target, & if not what can we do about it?' conversations with careful ring fencing from the fact that the previous evening the year 10 chap was babysitting the rest of our dc whilst the three of us were out on the lash.
It's a massive intensification of the usual crossover when you're all neighbours! 
But the basic principle stands. If one of my colleagues - who teach my dc - posted that picture, I'd think, as you do, that it's not one I'd put online myself - but then I'd conclude it's totally not my business.
I worry about my own online presence & it's carefully locked down. Students can easily find me because they, & I, will have all liked the official school FB, but all they'll see is a completely anodyne profile pic which I've run through Meitu because it's funny.
If a colleague had this profile pic I'd think 'well, I wouldn't fancy the ribbing from my Y11 tutor group - probably not a great idea' but it's not actually offensive or indecent.
Either there's more to this or school need to wind the neck in.