Hopkinson's use of St. Loyola's name could be in reference to St. Loyola's founding of the Society of Jesus. In "The Reverse Cheshire Cat", Prof and Loyola are similar to missionaries, but they are collecting stories, rather than spreading the Gospel. They are more like oral historians than missionaries, but Loyola's frequent surprise at the customs of the people they visit suggests that they share a different culture from the people they interview. Loyola does make reference to a church, presumably within the "M.A.":
Loyola’s pastor called it the annual culling of the herd, said if those people had been worthy in the eyes of the Lord, He would have granted them the means to afford the antibiotic injections.
However, the specifics of the church's religion are left ambiguous.
Throughout the story Loyola seems surprised by the discordance between the M.A. and what she sees in San Meander:
The woman waiting tables was plump and pretty. Was she… Mexican? Loyola whispered, “They let illegals work here?”
Prof sighed. “No assumptions. You’re not in the M.A anymore. Try to remember.”
Loyola and Prof are outsiders in San Meander. They are on a fact-gathering mission to add stories to their "compendium", presumably focusing on stories about viruses, given the allusions to various illnesses in the story.
The happiness that Prof and Loyola feel upon hearing of the strange allergies of the people of San Meander is puzzling, but if we think about it in relation to the characters' religion, which bears some resemblance to the notion of unconditional election, then their glee could be a product of how this story affirms their preconception of the sick as part of the unelect.
Consequently, the use of St. Loyola's name could be meant to spur these and other religious connotations.
Moreover, the use of St. Loyola's name could be partly ironic, as Loyola and Prof appear uninterested in saving the people of San Meander. Instead, they are content to simply gather their stories.