> any solution which involves active parent participation is going to get shunned by a vocal subset

Then we certainly shouldn't be passing laws mandating age verification. If parents want to abdicate their responsibility over their children, it's not the role of government to enshrine that abdication into law and take over the duty of parenting from them.

If regulation is to be had, then it should take the form of mandating websites and services provide privacy preserving tools for parents to use, if they want to use them. If they don't, that's on them. Everyone else needn't suffer because a subset of the population has chosen to offload their responsibility into the government and web services.