I don't think this discussion is about professional networking. It's about personal and social connections. If quitting Facebook makes you un-/under-employed then I think you're Doing Life Wrong.

GP mentions "severing" those connections, but I think that's even too strong a phrasing. There wasn't really anything there in the first place, so there wasn't anything to sever. Simply not reading someone else's social media posts anymore, when you didn't really interact with them outside Facebook (or for some people even inside Facebook) isn't really severing anything.