In The Crucible, the town of Salem is most certainly strict. The fact that they live according to Puritan law, which is very strict, illustrates where the rigidness of the town comes from. The town is ruled under a Theocracy (which means those of rank in the church hold government positions as well--the government is a combination of church and state).
Given that they follow the government blindly (because of how they have been raised and the power the government has over their ideologies), anything which the government states is a fact for the villagers. Therefore, they are gullible because they simply believe in God and trust that his word will keep them safe.
If the members of the government say that witches live among them, they can do nothing but believe it. The government officials are ministers of God and, according to Puritan belief, hold the truth.