It shall be the duty of school directors and boards of education, school inspectors, and other corporate authority managing and controlling any of the public schools of the state to suspend or expel from the schools under their control any pupil who shall:
(1) Be or remain a member, promise to join, become a member, or solicit other persons to join, promise to join, or pledge to become a member of any such public school fraternity, sorority, or other secret organization or society; or
(2) Wear or display any insignia of such public school fraternity, sorority, or other secret organization or society while in and attending public schools.