How do the various characters respond to the events of the story "A Very Old Man with Enormous Wings?"

For the most part, the old man (alleged angel) is mistreated and variously misunderstood. 

Even though the man has wings, Pelayo and Elisenda think he is a castaway from some ship. Their neighbor notes the wings and concludes that he is, in fact, an angel. The neighbor believes that the angel is part of some "celestial conspiracy" and should be clubbed to death, but in their wisdom (or indifference), the couple refuse to do this....

For the most part, the old man (alleged angel) is mistreated and variously misunderstood. 

Even though the man has wings, Pelayo and Elisenda think he is a castaway from some ship. Their neighbor notes the wings and concludes that he is, in fact, an angel. The neighbor believes that the angel is part of some "celestial conspiracy" and should be clubbed to death, but in their wisdom (or indifference), the couple refuse to do this. Still, Pelayo locks the man in the chicken coop, thus treating him like a farm animal. In spite of the miracle of finding a man with wings in their midst, the first responses are ignorant, dismissive, reactionary, and abusive. 

By the next morning, other people in the neighborhood have arrived and treat the angel "as if he weren’t a supernatural creature but a circus animal." Father Gonzaga arrives to find that even though these people are mistreating the old man, they offer suggestions such as making the old man mayor of the world or promoting him to a high official position. Gonzaga tells the people not to be naive (ingenuous) and that the old man might not be an angel. Now, he doesn't tell them to start treating the angel better (just in case he is an angel or out of common Christian decency). He simply says he will ask the bishop. 

In the meantime, Pelayo and Elisenda start charging people to see the old man (angel). They make a lot of money. Then a carnival arrives and the people flock to see a human spider. The old man is no longer the star attraction and he is abandoned. Pelayo doesn't clean or keep the chicken coop repaired. Even though the old man had made them relatively rich, he becomes like a burden to them. When he finally leaves, they are only too happy to see him go. Elisenda is glad "because then he was no longer an annoyance in her life but an imaginary dot on the horizon of the sea."