The narrative of the story "The Jilting of Granny Weatherall" follows the stream of consciousness style. This means that the sequence of events will not follow a traditional order, and the point of view may be shared by a first and third person narrator, as it is the case in this story.
This being said, Katherine Anne Porter purposely allows the confusion of "who does what", "who is who", and "who says what". This is a way to somewhat commiserate with Granny Weatherall's own convoluted state of mind as she slowly, but surely, approaches death.
Therefore, out of two possibly good conclusions, one of the most likely candidates to have "cursed like a sailor's parrot" is John, who would then become Granny's future husband. It seems that John was a guest at the wedding the day that she was jilted. This is possible because John appears mentioned within the context of this particular memory and appears with close proximity in the narrative as part of another hallucination. A second good guess could be Granny's own father. After all, he is the person who is physically closest to her the moment that she is about to faint during her wedding day. Isn't the father the person who "gives" his daughter's hand in marriage? Also, who but a father could get angry enough to curse "like a sailor's parrot" and to wish for the death of the man who jilted his daughter?
He had cursed like a sailor’s parrot and said, “I’ll kill him for you.” Don’t lay a hand on him, for my sake leave something to God. “Now, Ellen, you must believe what I tell you….”
Those feverishly angry words have to come from someone who deeply cares for and loves Ellen Weatherall. Some have come to conclude that this is actually an exchange of words between Ellen's father and Father Connolly! Regardless of the guesses, the reality is that the reader is not meant to know who exactly is who in the story, precisely to preserve the atmosphere of confusion and foggy memories that moves the plot forward.