Certifiably private networks would be unaffected.
The government can do that now. There are segments of the IP address space set aside for government use, and traffic on those segments flows through government controlled routers. They can filter any IP address they want, and there are probably regulations in place that state that government owned servers shouldn't be used as porn servers. The vast majority of the internet servers, routers, switches, and even backbone segments are privately owned.
Then I think we have reached common ground!
(-:
I'm all for restricting porn wherever we can so long as the action does not allow a general restriction on free speech.
I would not support banning publication of magazines or even private production of currently legal videos.
I do support the President with his faith-based initiatives that would have an effect on people's hearts. It is far better to reduce the demand for porn than to threaten liberty by restricting speech.