I guess it depends on what *you* mean by private, too, right? Most people just want to live their lives in peace, but transpeople have, perhaps, to be at least somewhat open about it. Hard not to be, as friends, family, colleagues etc are hardly not going to notice if you change from one gender to the other.
And then, on the other hand... well, how many television interviews with transpeople have you seen? I can guarantee that exactly 100% of them will include at least one question along the lines of "can you tell me what's inside your pants then?" As if that is a question people normally ask to anyone else.
What I'm saying is that I agree it shouldn't be nearly as big an issue as it is, but oftentimes it isn't the transperson who makes it one.