To me, the major difference between our society and that of Puritan New England is that we are much more into the idea of individual freedoms. We tend to think that individual people ought to be able to act in more or less whatever way they want to (in terms of their private moral choices).
In the context of this book, can you imagine people today stigmatizing a woman to this extent for committing adultery? They punish her with the stocks and with the further public humiliation of the letter all for what we would think of as a private, moral choice.
Today, we tend to think that people's moral choices are (in general) none of society's business. Puritans were just the opposite -- they thought that people's moral choices reflected on their society and would affect their society's prosperity. As the eNotes summary says
the Puritans required a strict moral regulation; anyone in the community who sinned threatened not only their soul, but the very possibility of civil and religious perfection in America...