In light of the exchanges of the combatants in the political arena, it is not difficult to understand this poem. In fact, throughout history, those who have been prophetic or who have seen what the real problems exist in the future have been considered "mad."
Emily Dickinson's clever and ironic poem seems more relevant than in her day. For, those who truly understand and explain situations or foresee situations to come are scoffed and treated as though they are foolish or narrow-minded or some other pejorative term. Yet they are those who have "divinest sense," though those adherents of conventional wisdom would call them "mad."
Dickinson's third line compares to what John Stuart Mill called "the tyranny of the majority":
Much Sense--the starkest Madness--
For, this is the thinking of "the Majority" that prevails, Dickinson states in the next two lines,
"Tis the Majority
In this, as All, prevail--
The Majority that prevails is the majority that tyrannizes others with its conventions to which they are forced to adhere or else be "handled with a Chain"; that is, be locked up or ostracized or vilified.
While they may easily be other interpretations to Miss Dickinson's poem, it clearly is about those who think independently and can perceive beyond the present or the appearance of things and assess what real dangers lie ahead for people. But, to the obtuse majority, these few perceptive individuals are "mad," and considered dangerous to the complacency and conventional wisdom of the majority.