I truly believe that most of the people who ARE leaving the state (and my wife and I know several) are conservative. The politics of the state are a major part of the reason we (and they) are leaving. At least our state legislature recently had some restraint and voted down giving illegal immigrants in-state college tuition at the state colleges.
I think the people who are leaving the state are young families with children, people who can't afford homes in this state, and that is a conservative constituency.
It's been pointed out time and again that Massachusetts transplants to New Hampshire are more reliably Republican than native New Hampshirites, many of whom have shifted their voting habits, but it seems like N.H. people still look to us to blame for their state's turning a little more purple.