In the fifth chapter, Antonio's mother is speaking to Antonio's Uncle Juan when she says"

"Ay Juan...I pray that he will take the vows, that a priest will return to guide the Lunas - "

Earlier, in the third chapter she says:

"Ay...if only he could become a priest. That would save him! He would always be with God. Oh, Gabriel...just think of the honor it would bring our family to have a priest..."

In both of these places in the text, Antonio's mother expresses her sincere hopes that Antonio will achieve an honorable position. Notably, the founder of el Puerto and of the Luna's place in the world was a priest. The priest is therefore the ultimate patriarchal symbol for this religious farming family. 

In this way, Antonio's mother's hopes for him are not general hopes drawn from her religious culture. They are hopes drawn directly from her family's history; the Luna's geographical history.

This ambition also represents a desire for continuity (of place and of tradition), which is prized in the Luna family. By becoming a priest, Antonio ensures that he will remain a Luna, faithful to Catholic traditions and to his (mother's) family's past.

In Bless Me, Ultima, what does Antonio's father say about becoming a priest?

Tony's father is none too excited about his youngest son becoming a priest.  He would be much happier if Tony would follow in his footsteps, and that of his brothers, and adopt the roaming, nomadic lifestyle of the Marez clan.  Tony's mother and father argue about his future early on in the story, when Tony has been shaken by witnessing Lupito's death:

"Be sensible!" my father stood up.  "The boy has not even been through his Catechism.  And it is not the priest who will decide when the time comes, but Tony himself!"  He stalked past me.  The smell of gunpowder was still on his clothes.

They say the Devil smells of sulfur.

Tony is still a young boy at this stage of the story, with much to learn, and is as confused as anyone is at that age.  It is this sort of raw template that is Antonio that Ultima has to work with.