Free Speech doesn't allow anyone to use that speech anyway they wish.
But for a public school to limit that speech they
must have valid reasons.
See.
Tinker v. Des Moines Independent Community School Dist.
https://en.m.wikipedia.org/wiki/Tink...chool_District
The court's 7–2 decision held that the First Amendment applied to public schools, and that administrators would have to
demonstrate constitutionally valid reasons for any specific regulation of speech in the classroom. The court observed, "It can hardly be argued that either students or teachers shed their constitutional rights to freedom of speech or expression at the schoolhouse gate."[4] Justice Abe Fortas wrote the majority opinion, holding that the speech regulation at issue in Tinker was
"based upon an urgent wish to avoid the controversy which might result from the expression, even by the silent symbol of armbands, of opposition to this Nation's part in the conflagration in Vietnam." The Court held that for school officials to justify censoring speech, they "must be able to show that [their] action was caused by something more than a mere desire to avoid the discomfort and unpleasantness that always accompany an unpopular viewpoint," allowing schools to forbid conduct that would "materially and substantially interfere with the requirements of appropriate discipline in the operation of the school."[5] The Court found that the actions of the Tinkers in wearing armbands did not cause disruption and held that their activity represented constitutionally protected symbolic speech.
