In what ways does the veil affect Mr. Hooper's relationship with his congregation?

The veil affects Mr. Hooper's relationship with his congregation because, initially, the sight of him is so shocking. The veil makes his parishioners quite uncomfortable: they doubt it really is him, they think he's gone mad, and they believe he's changed himself into "something awful." In fact, "more than one woman of delicate nerves was forced to leave the meeting-house" while Mr. Hooper preaches his sermon. And all these responses occur only as a result of the minister's appearance.
However, the content and effects of Mr. Hooper's sermon are influenced by the veil as well. As a result of it,

A subtle power was breathed into his words.  Each member of the congregation, the most innocent girl, and the man of hardened breast, felt as if the preacher had crept upon them, behind his awful veil, and discovered their hoarded iniquity of deed or thought.

Mr. Hooper's parishioners feel this sermon more deeply and personally than they seem to have felt any of his sermons before. They are certainly more affected by it, and they "hurried out with indecorous confusion, eager to communicate their pent-up amazement" at the change in Mr. Hooper. In short, he makes everyone nervous. Further, they never really get used to the veil, especially because they actually have a good idea of what it symbolizes—though no one will admit it to themselves, let alone one another.  Even his fiancee cannot abide it.