My students and I are stumped by this. Why did Poe allude to the Freemasons in the short story, "The Cask of Amontillado?"

Poe had many plot problems with "The Cask of Amontillado." Montresor had to get Fortunato into the catacombs beneath his palazzo without anyone recognizing him as Fortunato's companion. That was just one plot problem. Another was: What are the two men going to be talking about during all the time it takes to get from the street to Montresor's palazzo, down into the wine vaults, and through the catacombs to the place where Montresor intends to chain his victim to the rock wall? Poe has to fill up space with some sort of dialogue, and he doesn't want them to be talking about the Amontillado. The reason Poe doesn't want them talking about the Amontillado is that Fortunato might ask some very awkward questions and become suspicious when Montresor couldn't, or wouldn't, answer them. After all, Fortunato is the expert. He knows more about Amontillado than Montresor. Otherwise he wouldn't be there. So Poe invents some incidental chitchat to fill up time and space. For one thing, he gives Fortunato a bad cold and a cough.

“How long have you had that cough?”

“Ugh! ugh! ugh!—ugh! ugh! ugh!—ugh! ugh! ugh!—ugh! ugh! ugh!—ugh! ugh! ugh!”

My poor friend found it impossible to reply for many minutes.

Notice how this fills up "many minutes." Poe is filling up space with such dialogue. Then there is all the talk about Montresor's coat of arms and his family motto, to which many people have attached great significance. And there is the business about the Masons. But never a word about the big cask of Amontillado! We can assume that there is another reason why Fortunato doesn't bring the subject up. He doesn't want to show too much interest in it because he is secretly planning to play another of his many dirty tricks on Montresor.

It is pretty obvious that Montresor is in a big hurry to find out if his fictitious Amontillado is genuine. This must be because he got, as he says, a "bargain" and would like to buy more if he can be sure of the quality. Fortunato is not going to all this trouble to help a friend, or to show off his connoisseurship, or to drink a glass of Amontillado in a dank catacomb full of dead men's bones. He wants to get in on the bargain. But he too has to be sure it is genuine. He doesn't have to taste Montresor's wine for that purpose. He knows there must be a ship newly arrived from Barcelona with a cargo of Amontillado. He could easily find the ship and taste the wine on board. But he doesn't want Montresor going to Luchesi if he should refuse to accompany Montresor to his palazzo immediately. Fortunato is rich. He could buy the entire cargo. Montresor knows this is what he is thinking because this would be typical of the "thousand injuries" he has already suffered. 

So Fortunato can't talk very well because of his cough, and he isn't anxious to bring up the subject of the Amontillado because he doesn't want to show his strong interest in the possibility of making a lot of money. They talk about other things. One of the other things is the Masons.