Hopefully the HT will tell this young man that he is leaving himself open to all sorts of accusations if he doesn't lock down all of his SM.
I have worked with a simialr young man, also in PE. He was outraged that his human rights were being impinged upon... was absolutely detemined that he would not change how he used his SM in order to kow tow to anyone, HT, students, professional bodies, the law etc.
One young male student lodged a complaint about something relatively mild and the repercussions were far, far greater than I could ever have imagined. We, all staff lecturing and otherwise, wer reminded about our SM, given Conduct Guidelines to sign on pain of formal grievance etc. It isn't 'something of nothing' at all!
And that's before you get to what it is about him that makes the girls feel the 'ick'!
Stay with the HT on the social media thing. And support your DD in talking through why she feels uncomfortable and having someone else on staff to talk to, counsellors are good for such stuff, they are hard wored into ALL safeguarding lines.
Don't worry about the young man. If he is sensible, willing to learn how to be a good teacher apart form being an indpendent private individual, he will take the information well and lock his SM down and grow up a bit!