First each country has passport regulations as to how they identiy gender. Some will provide passports without SRS others will allow with your doctors letters. If your country allows this then get it done asap.
If you opt to go with the original passport then the picture must look like you, be it male or female. If not you will encounter delay as they throughly check out your ID. The US has laws that protect our rights but you also have to assit in making sure they can ID you. Best your ID also has fingerprints, and I'm sure you had your fingerprints taken. I always advise TG to ensure their ID include their fingerprint and also more hi tech - your DNA profile.
I fly around Asia ala male mode. I have long hair which is in a pony tail when I travel and after 18 months on HRT my facial feature have become softer BUT they can recognize me after a few deliberate looks.