This is like something out of the Circle by D. Eggers. If you haven't read it, it is the new 1984/Brave New World for the Millennial generation - or the part of it that reads at least.
I can't believe some employers think not being on social media is a negative thing, they must be brainwashed social media acolytes or surveillance control freaks. Regardless, you're better off not working for them.
Just look at the CNN meme-tastrophe. CNN knew full well that threatening to doxx a meme creator was effective, primarily because it has participated in riling up a load of violence-advocating anti-free speech zealots. Putting out his name would have been the equivalent of putting out a contract on his/her life.
If you are one of those not on social media and your employer asks why you aren't on social media, perhaps the best answer would be "I am not interested in using my real name or other identifiers on social media given the persecutory atmosphere regarding free speech and non-conformism."