The phrase "burning the stake" is a historical reference to the practice of executing people for crimes such as heresy and witchcraft. This act involved tying the accused to a wooden stake and setting fire to them in a public spectacle. Today, the phrase is often used figuratively to describe scenarios in which someone is being punished or ostracized for their beliefs or actions. Some synonyms for "burning the stake" include "shaming," "hazing," "outcasting," "condemning," and "persecuting." Each of these words carries its own nuances and connotations, but all speak to the idea of punishing someone harshly for their beliefs or actions.