The counter must be as visceral is the claim. They make an emotional pitch:your children are in danger, surveillance is the solution. The counter must show the dangers in visceral, emotionally relevant way. This surveillance is actually a risk to parents and children as well - that by the accusation of an opaque, unaccountable system, you will be labelled a pedophile, and your kids taken away. That when sharing a picture of your own child with your own mother, you will have to worry about what the electronic bureaucracy will label your picture as.
Abstractions like privacy,and categorical claims, aren't going to reverse this. A properly pitched campaign could do. Sure, complain that politicians and the public are dumb. That may make you feel better but it won't change this an iota. Talking to people in the terms they care about might.