Why is New Hampshire so "purple"?

[Dgov]

Well, they used to be a strong Libertarian state, but that's changing now, as Bostonites and some other New Englanders have started to move in.

As for why they were strongly Republican in the past, it was primarily because the state stayed generally as small and mid-sized town for most of it's History.  Nothing like the Liberal Boston or Hartford or New York culture ever took root there, and it avoided the Hippie immigration that took on most of Vermont and West Massachusetts.

[Dgov]

The main difference with Maine and Vermont is that it comprises the Boston suburbs, which are quite republican. Probably, rural NH isn't that different than Vermont.

Actually, New Hampshire is rather uniform in it's voting patterns.  it's one of only 6 states where every county voted for obama (HI, MA, RI, CT, and VT), and considering that he only won the state by less than 10 points, that's pretty even partisan distribution.

Though looking at the map, his best counties were the ones that border rural Vermont (60-ish) and his worst were the ones that border Massachusetts (51-ish), so you're probably right.