Strict adherence to the 'no parent /teacher FB friends' policy at the international school where I teach (& my children attend) would wipe out my entire social life*, & half my colleagues would have to defriend their spouses.
Common sense prevails: I'm only FB friends with colleagues with whom I have a RL friendship, not (for example) my dds' grumpy Maths teacher who hates me anyway because his PM review directed him to be mentored by me to help with his behaviour management.
Equally, one of my closest friends has a dd in my class this year. It would be weird to have de-friended her when we'd spent all last year hanging out together, chatting, getting merrily pissed together...
Agree this is peculiar to overseas/ small communities, or private schools where tuition fees are a teacher perk - things are usually tighter in the UK state system where most teachers live out of catchment & avoid this problem.
& I definitely use a fake name, refuse student friend requests etc.
*that sounds pathetic! Only because get togethers are all organised by FB or whatsapp, & if no one was in the same group with anyone else who taught their kid, the complications would go something like: 'right, I'm having a barbecue but I can't message Ann, Bob, Claire, Dave, Ethel or Fred - who IS allowed to contact them on here?' 