The enduring conflict of this book that is present throughout is the way in which Antonio feels pulled between the heritage of his father, who comes from a line of plain-dwellers who roam around on horseback, and his mother, who comes from the Luna clan, and represent a long line of farmers who live on the soft soil and base themselves there.
What Antonio realises at the very end of the book, is that the key divide he feels as he is pulled between the Marez heritage and his Luna background, and likewise between Catholicism and a more primal, animist religion as represented in the Golden carp, is that he does not have to choose one or the other. He can, in fact, choose to blend both together to form a new religion and a new identity for himself that is made up of both. Note what Antonio says to his father:
Take the llano and the river valley, the moon and the sea, God and the golden carp--and make something new... Papa, can a new religion be made?
Antonio thus sees the end of his identity conflict because of being able to blend his two backgrounds and key influences together into something new. It is no longer necessary for him to only pick one.
Can't do better than the answer given above. That nails it!