In the playThe Miracle Worker this particular scene refers to a poignant moment in which the Kellers were eating together, and Annie was struggling in the process of making Helen take responsibility for her choices at the table. At this moment Helen was throwing the napkin on the floor while Annie would get up and putting it back in the correct place. Through the tense meal, the family began to diffuse the situation and the topic of religion was coming up about what "The Good Book" said about certain things, clearly making it obvious that the Kellers were not necessarily "church fanatics".
To prove this, and to answer the main question, Aunt Ev mentioned that the reverend of the parish had been complaining that his hens are not laying any eggs. As part of the sarcastic comments that the family is known to make against religion, James joined in by reasoning that, if the hens are not laying eggs for the Reverend it must be because "they are Papists". What he meant by that joke was that they did not follow the Reverend's same religious faith, hence, they quit laying hens just to spite him.