I don't think she's touching the HS part, just collegiate because SD will have the NCAA on their ass.
My take is she got a bill from the legislators that wasn't vetted properly wrt to legal ramifications, and now she has to take a bath in it.
If she signed that bill, there would be a influx of trans to SD colleges demanding to play on girl's teams and an army of NCAA lawyers backing them up.
Can't stop this bullshit by legislative or legal means in this country as things are running now. People have to stop watching any college sports.