Actually 10% false positive rate is not that bad if the system really has a 90% chance of detecting child abuse. Keep in mind that it only raises a flag, it doesn't automatically results in a false conviction.

I don't have the numbers but I think that during an investigation, way more than 10% of suspects did nothing wrong. In fact, some people estimate that 10% of convictions are wrong (though I think that's an overestimate). A 90% effective system may actually end up preventing false arrests, search warrants, etc... a win for privacy!

The real concern is the potential for abuse, not that 90% bar that is, I think, completely reasonable.