Final answer:
The school district's decision to ban Nathaniel Yu from student government would depend on the specific circumstances and reasons behind the ban. However, students in public schools are entitled to certain free speech protections under the First Amendment, unless their speech materially and substantially interferes with the operation of the school.
Step-by-step explanation:
The school district's decision to ban Nathaniel Yu from student government would depend on the specific circumstances and reasons behind the ban. However, the general legal principle is that students in public schools are entitled to certain free speech protections under the First Amendment. In the landmark Supreme Court case, Tinker v. Des Moines Independent Community School District, the Court held that students do not lose their First Amendment rights to freedom of speech when they are on school property, unless their speech materially and substantially interferes with the operation of the school. Therefore, the school district would need to demonstrate that Nathaniel's involvement in student government would materially and substantially interfere with the operation of the school in order to justify his ban.