I just see it as an unnecessary hill to die on. Its not possible to win on those conditions so why spend energy on a failed outcome? I wish those who shared the sentiment found an effective method to achieve their goals, but online message board activism doesn't pass the sniff test.
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].
It seems like the example you give points to undesirable consequences as a direct result of government intervention. Is your example meant to be a point against any sort of legislation regarding age verification?
It's a general principle but too simplistic to contribute to a solution.
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.