To me it's a public health issue and shares the same, "you can do what you want, but I will not be forced into participating," that resulted in the invention of chin diapers. To an outsider both look like pathological demand avoidance[1].
1. https://en.wikipedia.org/wiki/Pathological_demand_avoidance
Surely you don’t support ID gating the Internet?
I believe I should prevent you from starving, willfully or negligently harming (in a serious way), or denying significant education or medical care to your childern; I believe you shouldn't be able to take your children into some adult places like strip clubs.
The strip clubs also have an obligation to keep out your children and need a method to do so, in this case the online 'strip clubs'.
The question is, given other priorities such as privacy, what is the best method? I think it's parental tools in OSes, including the ability to setup accounts for minors.