Hazelwood School District v. Kuhlmeier was a landmark decision enacted by the US Supreme Court in 1988 related to the applicability of the right of freedom of speech, granted by the First Amendment to the US Constitution, in curricular student newspapers in public schools. Lowers courts have sided unevenly with the students who sued claiming their right of freedom of speech and the school director who decided to remove two articles from the student's newspaper.
The US Supreme court ruled (and established the precedent for future cases) that school authorities could exercise prior-restraint in school-sponsored channels of expression, provided that it was justified by pedagogical reasons. Such student newspapers written in the schools are different from public forums for student expression where their constitutional right to freedom of speech should be guranteed with no limits.
Therefore, in the drama class described, and according to the ruling of the Supreme Court in the case detailed above, the principal of the school has the right to cancel the show if he considers it to be inappropiate for the children of that age (this would serve as the required pedagogical justification) as it would be part of school-sponsored channel of expression.