Child protection filters would work much better as browser extensions.
http://stackoverflow.com/questions/18447874/google-chrome-us...
I'm not familiar with how those typically work, but intuitively from an architecture standpoint, that sounds like something that should sit as a filter between the browser and the outside world. Browser as monolith of functionality seems undesirable.
With a browser extension (which you would also need to get installed on the device in some manner) you can inspect the pages as they are displayed.
In-path filters outside the trust boundary are, I'm afraid, the very first casualty in our efforts to mitigate the threats of nation state adversaries, as they resemble the attacks used there too much to survive. I, for one, will not mourn them.