The most important theme of "The Crucible" by Arthur Miller is Persecution. A second important theme is being Judgemental. Concerning the most important theme, Persecution, "The Crucible" deals with the vicious persecution of Elizabeth Proctor, accused of being a witch and practicing witchcraft.
The story is a lesson in how individuals can join with the aggressive masses and turn on those in their own community quite quickly when they perceive someone as being different or acting contrary to their beliefs and value systems. This story deals with religious leaders and the citizens of Salem attacking one of their own. Witchcraft, and its manifestations, have the town fearful, and they seek to punish individuals engaged in this practice. Therefore, they instituted the Salem Witch Trials.
The story is a take on what was happening in America at the time Arthur Miller wrote his story. Hearings to root out Communist sympathizers were taking place in the United States at the behest of Senator Joseph McCarthy and others. Miller used his story of the Salem Witch Trials desiring to root out witches as a way to discuss what was going on in America.
The secondary theme is being Judgemental. This theme deals with people in the town pointing their fingers at others, while not looking at their own behaviors that are vile. It's the classic "when you point a finger at others, you have three pointing back at yourself." This theme deals with getting our own houses (characters) in order before trying to clean up the houses (characters) of others.