The narrator uses the term "shrewd" ironically. Robin is not shrewd at all, although one could argue that by the story's end, he has become a little more discerning when he realizes that his kinsman, Major Molineux is reviled by the townspeople. So, at most, Robin becomes a little more shrewd by the story's end. But up until that point, Robin is clueless and naive in interpreting the actions and words of others.
At the opening of the story, the narrator notes that when Great Britain had begun to appoint their own colonial officials, the people of the colonies did not approve. "The people looked with most jealous scrutiny to the exercise of power, which did not emanate from themselves . . . " In other words, the people would have preferred to elect their own officials; so, they were inclined to resent Major Molineux.
As Robin makes his way through the town, he get hints from townspeople that they want nothing to do with Major Molineux. Robin, being optimistic and too proud of his connection to the Major, doesn't put this together. For example, when he is in the tavern, he believes the innkeeper's initial friendliness is because the innkeeper recognizes Robin's family resemblance to Major Molineux. However, when Robin finally mentions the Major's name, the innkeeper and the rest of the people in the tavern become hostile towards him. Robin shows a lack of shrewdness here because he thinks they turned hostile because he had little money. He doesn't understand that they want nothing to do with a kinsman of Major Molineux. Once again, the narrator is being ironic, even mocking Robin, when he uses the word "shrewd":
'Now is it not strange' thought Robin, with his usual shrewdness, 'is it not strange, that the confession of an empty pocket, should outweigh the name of my kinsman, Major Molineux?