When it comes to passports and medicare card, though, it is very easy to change the gender marker. So, if the birth certificate is a problem in your state, just get a passport with the new gender marker and you are done. You will never need to show the birth certificate again, just the passport will be enough to get the ball rolling on anything.
And to change the passport and medicare details, all you need a is a proforma letter from a doctor/psychologist indicating that you identify as gender F or M.