I had to compose it for a (likely not very influential) document on which a committee here is working, and I thought I'd share it with others. Please keep in mind that this is a very sketchy guide, lacking in the sort of nuance that would turn four pages into forty. It tries to be a summary of existing First Amendment law, and the likely implications from existing First Amendment law when the existing law isn't clear; though I necessarily had to make judgment calls based on what strikes me as the most sensible interpretation of the law in light of the facts as I see them, I am not trying to design the Perfect Constitutional Rule.
Please note also that this at times alludes to what should be dictated by broader academic freedom principles — which may well be more protective of student and professor speech than the law is — but does not take much of a stand on what those principles are; that's the job of another part of the memo on which I'm not working. Finally, note that I do not discuss here the very broad First Amendment protections that private universities enjoy with respect to government action (or the nonexistent First Amendment protections that private university students and faculty enjoy with respect to the private university's action).
Public universities are bound by the First Amendment. Thus, both public university students and public university teachers are entitled to some protection from discipline, firing, and other retaliation for their speech. In some areas, this protection is pretty clear and pretty broad. In others, it's relatively vague. Student speech outside the classroom and outside academic assignments. Most clearly, students generally may not be expelled, suspended, or otherwise disciplined for what they say in student newspapers, at demonstrations, in out-of-class conversations, and the like. The Supreme Court made this clear in Papish v. Board of Curators, 410 U.S. 667 (1973), and Healy v. James, 408 U.S. 169 (1972). Lower courts have followed suit, especially in the late 1980s and 1990s cases that have struck down student speech codes. See, e.g., Dambrot v. Central Michigan Univ., 55 F.3d 1177 (6th Cir. 1995); Iota Xi v. George Mason Univ., 993 F.2d 386 (4th Cir. 1993); UWM Post v. Univ. of Wisc., 74 F. Supp. 1163 (E.D. Wis. 1991); Doe v. Univ. of Mich., 721 F. Supp. 852 (E.D. Mich. 1989).
Of course, student speech may be restricted if it falls within the narrow categories of speech that's generally unprotected (e.g., threats of violence, personal face-to-face insults likely to cause a fight, or intentional incitement of imminent and likely unlawful conduct). Likewise, the university may impose a substantial range of content-neutral time, place, and manner restrictions, such as bans on the use of sound amplification that would be audible from classrooms. And the university may impose reasonable and viewpoint-neutral limits on student speech on "nonpublic forum" property, such as building corridors and the like.
Still, generally speaking, student speech outside the classroom and outside academic assignments is protected from university punishment, even if it's offensive, wrongheaded, racist, contemptuous, anti-government, or anti-administration. Of course, it's not protected from university criticism. The university is itself free to publicly speak to condemn student statements that university officials find to be unsound or improper. Student speech within the classroom. The Supreme Court has never faced this question expressly, but the logic of the Court's cases strongly suggests that university professors have broad authority to refuse to call on students, to punish students for talking out of turn, and to stop calling on students who insult other students. Purely passive speech, such as speech on T-shirts, may still be protected, see Tinker v. Des Moines Indep. School Dist., 393 U.S. 503 (1969). But oral statements, which can easily disrupt the class discussion, are within the professor's authority. Student speech in academic assignments. Evaluating students' academic performance necessarily involves making content-based, and often even viewpoint-based, judgments. Did the student give the correct answer? Do the student's arguments make sense? Is a student essay well-written, well-reasoned, calm, and rhetorically effective?
There are no Supreme Court cases squarely on the subject, and very few lower court cases, but First Amendment principles generally suggest that universities must have very broad authority to judge such student speech. This is especially so because judges often lack the competence to evaluate the quality of work in various disciplines; they therefore rightly defer to the judgments of academics who are better able to tell what's a good student paper and what's a bad one.
Naturally, academic freedom requires tolerance of a broad range of student viewpoints, so long as they are thoughtfully argued and pay attention to counterarguments. But judges generally stay out of such grading decisions, and leave their limits to professional ethics rather than to First Amendment law. Faculty speech outside teaching and scholarship. Government employers generally have considerable authority over the speech of their employees, much more than public universities have over the speech of their students. Generally speaking, an employer may fire an employee for the employee's speech when (1) the speech is on a matter of private concern, such as general small-talk, or the employee's concern about his own job conditions, or (2) the speech is so likely to disrupt the employer's functioning that the likely disruption outweighs the value of the speech to the employee and his listeners, or (3) the speech is made as part of the employee's official duties. See Connick v. Myers, 461 U.S. 138 (1983); Pickering v. Board of Ed., 391 U.S. 563 (1968); Garcetti v. Ceballos, 126 S. Ct. 1951 (2006).
Nonetheless, the Supreme Court has repeatedly stressed, including in university professor speech cases, that "our Nation is deeply committed to safeguarding academic freedom, which is of transcendent value to all of us and not merely to the teachers concerned," Keyishian v. Bd. of Regents, 385 U.S. 589, 603 (1967); Sweezy v. New Hampshire, 354 U.S. 234, 250 (1957). The Court may well ultimately conclude that the role of university professors is such that the normal government employee speech rules don't quite apply to them. As the Court pointed out in Garcetti (which held that speech made as part of an employee's duties is constitutionally unprotected), "There is some argument that expression related to academic scholarship or classroom instruction implicates additional constitutional interests that are not fully accounted for by this Court's customary employee-speech jurisprudence"; the Court therefore expressly declined to decide whether the Garcetti limitation on employee speech "would apply in the same manner to a case involving speech related to scholarship or teaching." See also Jeffries v. Harleston, 52 F.3d 9, 14 (2nd Cir. 1995) (likewise leaving open the possibility that "a faculty member in a public university[] deserves greater protection from state interference with his speech than [do other government employees]"),
And lower court cases have generally concluded that faculty speech outside teaching and scholarship is indeed quite broadly protected by the First Amendment from employer retaliation, so long as it is on matters of public concern. See, e.g., Levin v. Harleston, 966 F.2d 85 (2nd Cir. 1992). The courts seem to take the view that a considerable degree of debate, controversy, and even disruption caused by offensive ideas is an inherent part of the interchange of ideas in which universities must engage. See, e.g., Mabey v. Reagan, 537 F.2d 1036, 1050 (9th Cir. 1976); Adamian v. Jacobsen, 539 F.2d 929, 934 (9th Cir. 1975). Therefore, while normal employers are generally entitled to fire employees who have (for instance) offended customers or members of the public, universities are probably bound by the First Amendment to tolerate similarly offensive speech by teachers, at least outside the classroom.
Note that this applies to professors facing discipline that might affect their academic posts. Professors who double as administrators — deans, chairs, heads of institutes — may generally be stripped of their administrative positions whenever they say something that higher administrations reasonable see as likely to disruptive. See Jeffries v. Harleston, 52 F.3d 9, 14 (2nd Cir. 1995). Academic freedom may mandate that the professor keep his academic post, but not that he keep related administrative posts.