It's not that it would be illegal. In theory, there's nothing illegal about trans support groups sending mailers like this to every house in a state. Actual trans groups don't do this because we're fucking stupid. LGBT groups always operate on a model of "you come to us, we don't come to you." Trans groups don't run literal recruitment campaigns.

If actual trans groups did this, the political backlash would be immense. You start "messing with" people in their homes, reaching out directly to their children? If an actual trans group did this, they would be politically suicidal.

The allegation is that some third party is misrepresenting the actual work of trans activists. They produce a pamphlet that has actual information and resources in it. But this is the kind of information normally given out as pamphlets in groups and queer centers. You normally have to go looking for it. Or on a website that is explicitly trans or queer. The allegation is that they produced a pamphlet of true information but then used it in ways actual trans people never would. I'm not sure how specifically that maps to criminal fraud law, but it might relate to some statute involving undue influence on elections.