According to the podcast, the mayor definitely identifies as transgender. He made the transformation gradually, starting with the fingernails. Eventually he got breast implants. Not clear if he has had other surgery, but I'm not sure it matters. As you said, much more complicated than "a man in a dress."

The part I thought was interesting was his male neighbors, many of whom turned up wearing dresses to support him against the Rev. Phelps gang. This might not seem like a big deal in a sophisticated metropolis, but it's clearly not the kind of thing the residents of Silverton were accustomed to a few years ago.