She's not suggested she feels her kids are at risk as far as I can see it.
As I read it, she's said, privately - "my kids won't be coming anymore because the way you live your life doesn't match my view of the world, and I don't want my kids exposed to that view".
He's then escalated the issue publicly, trying to be a bit of a smart arse. Escalation because he brings up 'life and death' (he's a dance teacher not a bloody doctor).
I think she's a bit of a tit because of her views, and I think he's a bit of a tit for turning it into a crusade (far from the calm response that's claimed, he shared it on Facebook, and that is not in itself indicative of a calm response, that's a "look at me, I put that bigot down in style" boast), and for that reason, I think he's the bigger tit in this situation.
Had she posted her message publicly, I'd have a different view, but there's nothing to indicate that is the case.
I think she's wrong to deny her kids the opportunity of learning with a well respected teacher because of an irrelevance such as the sexuality of the instructor, but I don't think her private message to him to inform him of her decision was wrong in itself; it was truthful. A better response would to have been respond in private and educate her.