One of the overriding theme of Marquez' parable is that people give lip-service to a belief in God but fail utterly in practice. The predominant symbol is the angel's wings. Remember, the subtitle of the story is "A Tale for Children." Like other fairy tales, this one has an implicit moral: that moral is to recognize the work of God whether it meets human expectations or not.
When Pelayo and Elisenda finally get up the gumption to inspect the miracle that has literally befallen him, they are more repulsed than awed by the angel and quickly subsume the miraculous occurrence into their psyches, by
"skipping over the inconvenience of the wings and quite intelligently concluded that he was a lonely castaway from some foreign ship wrecked by the storm."
Pelayo displays his lack of faith my refusing to acknowledge a true miracle. Over and over the characters cannot reconcile the "logic of his wings" because they do not meet with their human expectations.
Pelayo is not alone in his lack of faith. The priest is no better. When the angel does not understand Latin, the priest concludes that the angel is an "imposter" because he did not speak "the language of God."
Elisenda, who comes up with the plan to charge visitors to see the angel, eventually shouts that "it was awful living in a hell full of angels." What she really means is that it is impossible to live by faith and not reason.
I don't see any evidence in the story that Pelayo does not believe in God. On the contrary, you can say that he does believe in God but that he is not very reverant. For one thing, Pelayo and Elisenda don't seem shocked to find a winged man in their chicken coop. Immediately, they think he is an angel that has come to take their baby away. Another reason for thinking Pelayo does believe in God is that he calls in the parish priest to examine the "angel" and give them advice on what to do with him. Father Gonzaga consults the pope about what to do.
Maybe because the only thing that makes the old man angelic is his wings, and even they are scraggledy and buggy. Maybe that's why they use him as a cash cow.