Here's the thing. It is up to an entire culture to decide what is and isn't normal. I personally have no problem with transgendered people (other than being horrible with pronouns). There was a math teacher at my university who was a guy but preferred to wear a dress, no real issues anywhere in it. Fact is in the end it really is sexism. Why can't a man wear a dress, or a woman uh not wear a dress. Really there seems to be no problem with women wearing clothing more like guys do but when it is a guy in a dress all the sudden it is an issue....
To me transgender just means the person doesn't see the boundary that society has set for mainly arbitrary reasons. It is really just different, not a problem. The fact that something like choice of clothing sets people off this far just annoys me.