This speaker doesn't mind telling people how she feels. She doesn't mince around the topic at all. She launches right into it, and tells us exactly what she thinks. To wit: to her, mainstream society is nuts. And to make matters worse, it's too nuts to know it's nuts, and it oppresses people who have the courage to point out how nuts it is. Yikes.
Now, it's not nice to make assumptions about people, but we figure it's a safe bet that the speaker feels like one of those insanely sane few who's oppressed by the mainstream. Rather than being all mopey about it, she lashes out it in a biting, almost sarcastic way. She's fed up with what she sees around her, and she's letting us know about it.
The speaker never specifies her race, social, or even gender—so we really shouldn't necessarily call her "her." By leaving the specifics of the speaker kind of general, Dickinson lets us imagine who the speaker might be. Of course, the speaker could be a reclusive poetess in New England, but: yawn. The speaker could also be the voice of the many oppressed groups in Dickinson's time—African Americans, American Indians, women of every race. In other words, the speaker is the voice of the underdogs, the misunderstood, those whom the Majority keeps under its thumb. Whoever the speaker is, she's mad as hell, and she's not going to take it anymore.