Unfortunately the answer to this is unclear. So far only one state — Virginia — has passed a law allowing public colleges and universities to filter the Internet.
In 1996, Virginia passed a law that “restricts access by state employees to lascivious sexually explicit material on computers owned or leased by the state.”
Access to such material may be allowed if it is part of an “agency approved research project” and permission is granted by a supervisor. The law was challenged by six state university professors on grounds that the law unconstitutionally interfered with their research and teaching.
The case was heard by the full 4th U.S. Circuit Court of Appeals, which in an 8-4 decision, held the statute to be constitutional. The court had to determine if the statute regulated speech made by public employees, in their role as private citizen, on matters of public concern. The critical determination, according to the court, “is whether the speech is made primarily in the [employee’s] role as citizen or primarily in his role as employee.” The court found in its 2000 ruling in Urofsky v. Gilmore, that the speech at issue — “access to certain materials using computers owned or leased by the state for the purpose of carrying out employment duties” — was clearly made in the employee’s role as employee. Therefore the statute “does not affect speech by [the professors] in their capacity as private citizens on matters of public concern” and thus “does not infringe the First Amendment rights of state employees.”
The professors in Urofsky had also argued that the statute was unconstitutional because it infringed on their First Amendment right to academic freedom. The 4th Circuit judges rejected this argument, saying that their review of the law lead them to conclude that the right to academic freedom was held by the university and not the individual.