Symbolism, Imagery, Allegory
Like most of the imagery in The Power and the Glory, alcohol has opposing meanings that are actually complementary. Like yin and yang. Bert and Ernie. Biggie and Tupac.
On the one hand, alcohol is a sign of the priest's drunkenness. It's an image of sin. The term "whisky priest" is not a compliment (1.2.85). His drunkenness also affects his job. We hear a rumor, mostly likely true, that the priest performed a baptism while drunk and gave the child the wrong name: Brigitta instead of Pedro (1.2.82)! Oops.
On the other hand, alcohol is a sign of the priest's mission. He needs wine to celebrate the Mass. He can get by without the book and the altar stone, but without the wine there's no Eucharist. Aside from hearing confessions, there's nothing he can do that the laity (Catholics who are not clerics) couldn't do.
These two meanings come together when the priest tries to buy wine from the police chief's cousin only to leave almost empty-handed because the chief's cousin, the chief himself, and the beggar who introduced them all drink the wine before the priest can leave with it. He has to leave with a little brandy. And, of course, he gets arrested for having it in his possession.
Poor guy. He was trying to be good.