Pur·i·tan·i·cal

Strictly religious or moral; practicing or advocating rigid standards of behavior, especially related to self-discipline and modesty.

The teacher's puritanical rules banned music, dancing, and even colorful clothing in the classroom.

strict · austere · moralistic · rigid · self-restrained

From Puritan (17th-century Protestant reformers) + -ical, referring to their often severe moral codes.