It does seem like a two-edged sword. On the one hand, it's good to see trans being visible - but on the other, it does kind of imply that you're either man/woman, or you're trans. A "fill it in yourself" option is ideal, I think.
It does depend on what the organisation is, and how they're going to use the info. In some cases, I'd put trans just to help them be aware of how many trans people they're catering for - this can be valuable for public services, sports centres, stuff like that, as it makes them pay more attention to the services they provide, and how sensitive they are to trans people's needs.
If it's something more personal, I'd have to choose on a site-by-site basis.