That's a popular misconception; an understandable one, though because we all know about Massachusetts' tendencies, but still not true.
The two most conservative counties in NH (which contain about half the state's population) are along the Massachusetts border. Our liberal loons are more focused to the west (closer to Vermont, in the college towns of Keene and Hanover and in Peterborough) and in Portsmouth, along the Maine border. Also the state capital, Concord (unionized government employees).
According to the census in-migration studies I've seen, many of them came here from NY, NJ, MD, DE and PA. And I did look it up because I wondered where the hell these nuts were coming from. Massachusetts more frequently brings us its refugees (I'm one of them)... and bad drivers, too, but that's another story.
You know better than I do. I try to stay north of Conway. I get that far south and see as many Mass. plates as N.H. plates.