You must remember that the contents of libraries have always been "censored", though perhaps the better word is "selected".
For younger readers, books are selected appropriate to their reading skill as well as their age. Most 12 year olds would not know what to do with ancient literature written in the original Greek or Latin, and such books would be inappropriate for them.
A second consideration is book quality. There are lots and lots of books out there on any given subject, including "vanity" books published by the authors themselves. Quality varies dramatically. Libraries attempt (not always successfully) to use generally respected and quality works.
Lastly, some common sense is applied. Should a children's or school library really contain books on bomb-making or other extremely intense subjects?
As to the Internet: There is a great deal of mis-information out there, some of it even dangerous. Anybody can set up a site and put anything they want on it; that by no means makes it authoritative or appropriate. Even legitimate organizations screw up on their Internet sites by failing to keep the information timely and accurate.
As mentioned, student "access" is already quite limited in many ways.