The New Hampshire politicians have already shown their bigotry and prejudice by unjustly criminalizing zoosexual sex (interspecies sex) earlier this year when they made a brand-new oppressive and unjust anti-zoosexual law, so it doesn't surprise me that they aren't entirely doing what they could to support LGBT. As far as I'm concerned, there's too much prejudice and bigotry in New Hampshire right now.
The NH politicians apparently think that oppressing and persecuting zoosexual people is a higher priority than other things. The new anti-zoosexual law is state-sponsored discrimination.
With regard to LGBT, as I said, NH is not as progressive as other states, though it was one of the first to legalize gay marriage. In a number of categories, New Hampshire is mediocre, and its "personal liberty" ranking has been progressively getting worse each year.