I'm not a parent so I've never looked into this, but every time I hear someone like this woman ranting about ratings. This could be solved a lot differently if we added something to HTML specifications. A meta tag be it. A company who feels their website is safe for children could add the meta tag to their website that says it is for purposes of this conversation "GA", "PG", "R", "X". Mandate that any site that displays pornography rate their site. The browsers then have parental controls added that basically say this browser can only access certain material if a password is entered. If a site fails to put the tag it is treated as X by default.
It would be the responsibility of the parents to make sure the access controls were configured properly on their children's devices.
Google could then when it does searches get this setting from the browser and only return content with the correct tags.
No external rating board needed.