I would think that this is still an area in definition. There will be much in way of debate and discussion on it. From a pure libertarian point of view, any infringement is too much infringement. Any external monitoring is going to take away from the freedom of the individual. Yet, as the internet and technology advances, perhaps new paradigms need to be understood and appreciated in such realms. There might be some limitations needed, especially given how children can easily access what is present on the web. At the same time, this cannot be the only answer. Parents, teachers, and other adults have to constantly be in discussion with children to inform them as to proper use of freedom. In the end, the policing of the web is an issue that is under constant reexamination and analysis, as the realm is still relatively new.
One way in which policing can go too far before infringing upon the freedom of the individual is when the person conducting the policing uses additional methods from the usual way of policing to access more information than needed. For example, if the IT person at a school is tracking down how students and teachers are surfing the Net, the only information that person should be looking for is whether the use of the net is done for school purposes. If that IT person uses his or her privileges for password retrieval, etc. to access other information of the individual, then certainly that would be infringing upon personal freedoms and rights.
Of course, any policing infringes on the freedom of the individual. If you tell me that I cannot look at child pornography on the internet, you are infringing on my individual freedom, for example.
So the question really needs to be how far policing can go before it infringes too much on the rights of the individual. This, of course, is a matter of opinion and it is very hard to specify how far policing can go.
Personally, I think that it is fair to police the internet to try to prevent it from being used to commit crimes. I even think it is acceptable to try to police it to prevent copyright violations.