While the setting definitely contributes to a theme of decay and a foreboding mood, I don't think that the entire society presented in this story can be thrown under the same wagon as Tom and his wife. While there are surely some general and specific crimes or instances of poor morality mentioned, Tom and his wife are not representative of society as a whole, and this story still serves as a fable or moral cautionary rather than an apocalyptic social commentary.
The most distinct elements of setting that contribute to this theme are the swamp with the ruined Indian fort, and Tom's dilapidated house. The swamp has several images that directly and indirectly convey a theme of rot and decay, and Tom's home does the same for sterility. The trees that represent people, particularly the one for Deacon Peabody, are probably the most direct link to the idea of the setting depicting moral decay, as the deacon's tree is rotten on the inside, metaphorically depicting the same rottenness inside the deacon.
This is also the only point where we can make a direct connection to the broader society; Tom sees many trees, all of them marked with prominent names, and all of them scored with the Devil's axe, as if each chop is a strike against their character. However, the exact meaning of the axe scores is not given, and it is unclear if these represent some specific act of immorality, or if the amount is any more or less than might be expected. This also does not represent decay in as clear a manner as the literal rotting of the Deacon's tree.
So, there is probably not a theme of pandemic immorality in this society, but rather that the Devil is like a woodsman; carefully selecting his targets and nurturing them to his own ends. The average person does not seem to be very corrupted, nor particularly interesting to the Devil.