I think Vermont is the oddity rather than NH: if that state did not have its peculiarities, we would just say that modern New England has conservative rural areas (though more independent than other rural regions), swingy postindustrial towns and left-wing urban centres.
Vermont was one of the staunchest Republican states in the union until the nineties. The home of Yankee Republicans who were nonetheless liberal. The Northern equivalent of Alabama/Mississippi being Democrat hotbeds until the mid-60's.
