Heterodox is from the Greek root words heteros, meaning "the other," and doxa, meaning "opinion." The adjective heterodox was first applied to people who held a different religious opinion from the standard beliefs and teachings.
Today, although the religious meaning remains, the adjective heterodox can describe someone who adheres to any atypical beliefs, such as scientists who buck the current thinking or politicians who do not toe the party line. The word can be a synonym of heretical, which describes someone with contrary beliefs. If you are a teacher with a heterodox teaching style, you may win over students but alarm your more traditional colleagues.