In Gabriel Garcia Marquez' "A Very Old Man with Enormous Wings," the story seems to be a parallel to the story of Christ. Symbolically, Father Gonzaga represents the high priests that do not believe that Jesus is the Messiah. They tested Jesus often to prove that he was anything but the promised deliverer for which the Jews had waited so long. We see Gonzaga's suspicions when the priest tries to speak to the old man with the wings—deciding eventually that because the old man didn't look like an angel, he could certainly not be one.
Alien to the impertinences of the world, he only lifted his antiquarian eyes and murmured something in his dialect when Father Gonzaga went into the chicken coop and said good morning to him in Latin. The parish priest had his first suspicion of an impostor when he saw that he did not understand the language of God or know how to greet His ministers. Then he noticed that seen up close he was much too human...
This is very similar to the story of Christ. He did not act the way the Pharisees and priests of the Sanhedrin expected of him; when they asked questions, he answered with questions of his own. He did not condone the actions of the wealthy priests, and he consorted with tax collectors and harlots. Because he did not act as they expected he should, the religious leaders of the time rejected Jesus.
This kind of rejection is also seen in the old woman who comes to see the old man. She believes he is an angel, but shows him no deference or respect. The townspeople do the same—
...when they went out into the courtyard with the first light of dawn, they found the whole neighborhood in front of the chicken coop having fun with the angel, without the slightest reverence, tossing him things to eat through the openings in the wire as if he weren't a supernatural creature but a circus animal.
The people symbolize those who rejected Christ and demanded that he be put to death.
...incorporates magical or supernatural events into realistic narrative without questioning the improbability of these events...
It seems that the townspeople already believe that a woman in the circus was changed into a tarantula for failing to obey her parents. The priest warns the people that...
...the devil had the bad habit of making use of carnival tricks in order to confuse the unwary.
The people want to believe in the supernatural and the magical; sick people come to see the "angel-man," with hopes of healing. Even so, the old man does nothing to validate their beliefs in him.
His only supernatural virtue seemed to be patience.
The people torture him, like Christ was tortured with the crown of thorns and the whipping. They burn his side thinking that he is dead. He is roused—with tears in his eyes—and he flaps his wings. If he is indeed an angel, no one treats him as such.
Perhaps the challenge of religion here is the same challenge Christ faced with the people of his time. This story may not be so much about a challenge to religion, but may reflect the challenge of the world against things related to religion: people find it easier to believe in the magical rather than the divine. Things supernatural and/or magical (like the "spider woman") are taken more seriously than the angel. And as a piece of magical realism, the supernatural presence of the "spider" woman is accepted, without real concerns with regard to how she can even exist.
The problem is not religion, but the people's lack of faith.
This is an excellent question. Clearly, the main person or character who stands for religion in this story is Father Gonzaga, whose career as a woodcutter before becoming a priest gives him rather a robust and no nonsense view of life. Note how he responds to the mysterious figure after he fails to respond to his greeting in Latin:
The parish priest had his first suspicion of an impostor when he saw that he did not understand the language of God or know how to greet His ministers. Then he noticed that seen close up, he was much too human...
The obvious inability of Father Gonzaga to successfully interpret the presence of this mysterious figure shows the ignorance of the church in understanding and interpreting what lies beyond the realm of its experience. Marquez is playfully parodying the church through Father Gonzago and the symbolism of the man with enormous wings. The story shows that the church, just like the other villagers, is incapable of coming to a logical and sensible conclusion about what the man might represent. Religious belief is shown to rely of ignorance and the fear of how ignorance might be perceived just as much as the other beliefs of the villagers.