Is the Scarlet Letter an allegory written by Nathaniel Hawthorne about the age in which he lived?
Hawthorne himself had transcendentalist leanings which would lead to his very definite opinions about guilt and sin. He definitely shows through this novel his opinions about obsession with sin and human weakness as well as the virtual self indulgent guilt which can result from such extreme self-hatred. In addition, Hawthorne's ancestors were Puritans and in fact participated in the Salem Witch Trials as judges. They were complicit in the execution of many innocent women. It has been suggested that Hawthorne felt some guilt himself over his ancestors' crimes and used this story to examine the results of judgement without forgiveness or self-awareness.
Interesting question. I would say no, not primarily.
Hawthorne knew a great deal about the American colonial period, and the book is first and foremost about that period. It is secondly about humanity in general—the tendency to exile the sinner, to by hypocritical, to deny the evil in ourselves. As such, it would apply to his time (and to ours), but wouldn't mainly be about his time, no.