What is the likeliest reason that the townspeople react so strongly to the veil?
The intentional meaning of the people's reactions to the veil, taken from the perspective of the author, is that they will see in his veil the reflection of their own sins. Also, they will take a good hint that, if the minister had the nerve to call himself a sinner, then they should be doing the same ten times more, and they haven't done so. It is meant to be a message to shock the townspeople. The minister's introspective look at his own life is meant to be a model for others to equally visualize their lives and determine to which level they are living up to the standards of any other church-going folk. The minister is also trying to demonstrate that anyone can sin, and that admitting to weakness and sin is an act of courage, which many may or may not like, but yet is a reality in everyone's life. In not so many words: Nobody is 'holier than thou.'