This page tests whether the Prefer: safe HTTP header is sent.
Your current setup does not send the Prefer: safe header.
The Prefer: safe HTTP header is a proposed standard way of informing a webserver that the user wishes to be served unobjectionable content, which is the case when parental controls are enabled.
Do note that this comes with the downsides of an additional bit for user fingerprinting, as well as informing the server of the fact that the user is probably a minor. I have also not yet done any testing to check how many webservers actually read this header to alter their responses.