To get an answer to this question, look at the narration that Miller places in Act I, Scene 2 after Rebecca Nurse enters the room. This will give you Miller's assumptions about why people resent the family.
The first major reason people might dislike the Nurses is because they have a lot of land. There have been disputes over some of the land. In addition, Francis Nurse used to be poor and is now pretty rich. There may be resentment over that.
The other major thing going on is political. The Nurses and the Putnam family were on opposite sides of a dispute over who should be the new minister in Salem.
pohnpei is right, but there's more, at least as far as Ann Putnam is concerned. She's a woman who has lost, what, seven children? That'll drive any woman crazy, and to make her suffering worse, Rebecca Nurse has never lost any child or grandchild. Ann is horribly, horribly jealous of that, and when Rebecca condescends to tell her how to raise her one surviving child in Act I, that just twists the dagger.