There is definitely a sense of prejudice among the characters in A Streetcar Named Desire which could embody the idea that "try as we might, we are unable to reconstruct the opinions of others".
Blanche calls Stanley a "Pole" against his wishes to be deemed as a typical American. She is also adamant that Stanley should change his ways and become what she would deem as a "beau" to her sister, Stella. In more than one occasion Blanche imposes her ideals onto Stanley, which is primarily what drives him mad enough to hold grudges against her.
However, Stanley also seems to hold a pre-conceived notion of American Southerners, seeing them as snobby and anachronistic. This is the reason why he sets out to find out about Blanche's past to see if her dignified and demure ways have any basis at all.
This being said, the characters of Blanche and Stanley certainly reinforce the idea that "try as we might, we are unable to reconstruct the opinions of others". From the moment that they meet, they obviously dislike each other; Stanley could not stand the dress and behavior of Blanche, and Blanche could not stand the appearance and behavior of Stanley. Moreover, they held each other liable for each other's backgrounds; Stanley would always pin the South on Blanche just as Blanche would pin the Polish background on Stanley. It is understandable, however, that the two strongest characters would not be able to co-exist being that the two are so extremely dominant and toxic. Henceforth, it is no wonder that, in the end, the play becomes a battle of survival for the two of them.