The countermove is what D-ID (YC funded, IIRC) said they would do and then changed their mind: train a face recognition library to generate modified versions of a picture such that a human would still believe it's the same person, but different enough that face recognition systems think it's someone else. Then use those pictures in all of your internet socials.

Edit: according to this article they did develop that, but they don't offer the service to individuals: https://techcrunch.com/2018/09/05/d-id-launches-its-initial-...