[Chapter 2 spoilers]Imo, Chihiro is not transsexual. His reason for cross-dressing wasn't identifying with the feminine sex but as a refuge for his insecurities of not conforming with the male stereotype, something that he was willing to change.
Now, the Japanese society is hardly the most progressive when it comes with this kind of topics but it imo it wasn't handled badly here. Much more egregious examples of homophobia and transphobia at the Japanese media aren't hard to find.
I agree.
The background story on Chihiro showed that he was always being made fun of for being a frail boy, so he took advantage of his androgynous looks and the fact that society didn't hate on girls for being frail/weak and decided things would be easier for him if he pretended to be a girl. In case there were any doubts that he wasn't actually identifiying himself as a girl, the whole thing that happens in chapter 2 is related to Chihiro confiding his secret with Mondo and asking him to train him so that he can become stronger, regaining his self-esteem as a male in the process.