Parris allows the Putnams to visit him because they have a casual friendship. This means that they maintain a certain amount of contact, even in adverse situations.
Although you have not shown the text to which this question refers, we can see from the context of the question that it refers to the play "The Crucible."
When reading the plot of this play, we can see that Parris and Putnam maintain a certain friendship. You can see this because:
It is important to remember that "The Crucible" is intended to represent the moments of mass hysteria that occurred during the Salem witch trials.
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