I don't know if you've ever read any Bill/Declaration of Rights, but they all have "this right shall not be violated unless the law allows it" provisions. Many of them even have "oh, and requiring state licensing to exercise such right is not violating it" provisions (see e.g. "This Article shall not prevent States from requiring the licensing of broadcasting, television or cinema enterprises" in Article 10 of ECHR).
The 4th, 5th, 7th do have such provisions. And despite the 1th amendment prohibiting the Congress from "abridging the freedom of speech, or of the press", both war-time censorship and prohibition of pacifist/anti-war propaganda has been found to be constitutional during the WWI.
