Hey I went to Mexico (Cancun) back in April. I traveled in full feminine mode, wearing a dress, etc. My passport still says Male, but I had no real problem. The only small bump was going thru the body x-ray machine at the Philly airport ( the one where you put your hands over your head). When I came out of the enclosure the TSA person (female) stopped me and had me go back and redo it. When I came out again she had a puzzled look on her face. I turned around and looked back at the machine and at about mid-height were two little stick figure displays, one male and one female. The female one was illuminated and it showed a red x or circle - i don't remember - in the groin area. 'Aha' me thinks, I turned to the TSA agent and said "I'm transgender". Her eyes immediately glazed over, and waved me on, focused on the next traveler. And that was it.
All the airline counters, TSA agents, customs, Mexican immigration, etc. nobody cared.