I think the interesting part is that it's kind of counter-culture but it itself is not really a culture at all. There are no groups (as far as I know) for people who eschew social media. They don't meet up at the pub and talk about it, they don't have any kind of organization, even a loose one. People just kind of decide to wash their hands of Facebook and Instagram and Twitter and such, then go about their lives. I don't think they generally feel a part of some larger culture (or counter-culture)
Maybe I'm wrong about that. To me though it almost seems like a stand-alone complex.