West Virginia State Board of Education v. Barnette, 319 U.S. 624 (1943), is a decision by the United States Supreme Court holding that the Free Speech Clause of the First Amendment protects students from being forced to salute the American flag or say the Pledge of Allegiance in public school. The Court's 6–3 decision, delivered by Justice Robert H. Jackson, is remembered for its forceful defense of free speech and constitutional rights generally as being placed "beyond the reach of majorities and officials."
So this has nothing to do with a student from being dismissed from a school team or squad. Zero.