This map seems like a more trans-specific version of the one the ACLU is using to track anti-LGBTQ+ legislation: https://www.aclu.org/legislative-attacks-on-lgbtq-rights.

NH has some protections on the books: https://en.wikipedia.org/wiki/LGBT_rights_in_New_Hampshire, but not as many specific callouts like, say, neighboring Vermont.

A few state legislation bills show up every year trying to roll some of them back, or introduce groundwork for later attempts (like trying to define biological sex in a way that erases intersex people, for instance). Similar to what's happening in other states, though the bills tend to not advance.

Since Roe/Wade was overturned, trans issues seems to be the next big wedge issue everybody can rally around. Hardly anyone knows a trans person, it's very easy to "other" them, and there's an astonishing amount of misinformation out there about it. Kind of sucks, because we've plenty of other problems we could work on in NH that would improve the lives of more people.