I'm biased, but I would say to Google "Free State Project" or "The Shire Society" (inspired by Tolkien's hobbit town). It's all about people relocating with purpose and the people I've met through it are some of the most consistently accepting of LGBT of anywhere I've lived (GA, ID, SC, CA, MA). Been here in NH for 5 years now and it's been the best 5 years of my life.
I wouldn't say New Hampshirites in general are especially LGBT-friendly, but more than you would expect for a largely rural area. It is New England, after all. People who moved here for the FSP are, however, and that's how I've made most of my friends. I would say about NHites though--they are very friendly in public and generally have an attitude of respecting other people's privacy and staying out of their business.