tony's beliefsthe three beliefs tony is struggling with are catholisism, the golden carp, and ultima's magic. in the end, which religion does he choose?
The conflict between Catholicism in the traditional sense, and Ultima's more native approach to Christianity and healing is central to the book. It is also common throughout the American Southwest, both at that time and even today. That is why Catholicism in that region is markedly different than what you would find in Europe today--it is a mixture, that is, of native and Christian beliefs.
Tony, along with many, many others in real life, sees no reason to have to choose between the two. As generations before him have done, he finds a way to reconcile his Christian faith with his healing beliefs, just as Ultima had done.
It is important to remember that at the end of the novel, Antonio sees that he does not have to choose between different religions and the different heritages of his parents, but he can combine elements of all of them into his own identity. One of the most important messages of the story is the way in which we are not pushed towards absolutes. Antonio, after a discussion with his father, sees that he can form a composite identity, selecting bits of the different heritages and traditions that he struggles with to form his own sense of religion and his own sense of self.
In terms of Ultima's faith and the Golden Carp, remember that Ultima is a curandera, a natural healer, perhaps more native than Mestizo, and so the myths and legends associated with the people and the village have been a part of her belief system for her entire life, and make up the core of who she is. She is the spiritual counterbalance to that which is Catholic in Tony's life.