The cost of living in New Hampshire is lower than that of Massachusetts, and it's not that different from the two other northern New England states in terms of political quirkiness. NH has a mavericky/somewhat libertarian streak to it, and yes, many people from Massachusetts moved there and brought their cultural liberalism with them but not the desire to pay more for services or necessities. As for abortion, I would suppose that many if not most people in New Hampshire could just drive to a neighboring state if they needed one. They are more apathetic to the social policies of the NHGOP, so Sununu was able to sign some abortion restrictions while retaining goodwill thanks to his incumbency and retail politicking, not to mention the family name.
Sawx knows his state like the back of his hand, so maybe he would be able to provide a better explanation for this.
It also borders Canada as well. Many people work in Mass and live in NH as well.