You are aware that trans-gender is not just MTF, aren't you? You do know that there are FTMs, too. And I would suppose you'd understand that the latter would be a terrible disadvantage playing on the sports teams of the gender they identify with.
Look, I don't have answers to all these questions. The only thing I know is that good and caring people would at least TRY to find answers that do the least harm to the most people.
On a side note, as a gay male, when I played sports in school, I of course used the boys' shower and locker rooms (my highschool was an all-male boarding school, so of course no girls' showers involved). But think about it -- I had all the "eye-candy" I wanted. How do you think many of those boys, back in the 1960s, would have felt if they knew what thoughts were racing through my adolescent brain?
My point -- life can be confusing and messy. But we all know what male and female parts look like, and I can't for the life of me understand why everybody gets so crazy messed up about it. A couple of months ago, I was at the opera (Beethoven's Fidelio, if that matters) and standing at a urinal during intermission when a woman came out of one of the men's stalls and went to wash her hands immediately to my left. I understood immediately what was going on -- women can have terrible lines for bathrooms in theatres and so forth because it all takes them longer, and nobody thought that they should therefore have more facilities -- so I really wasn't bothered at all. She was probably in urgent need, relieved herself the only way she could -- and nobody was hurt. We humans need to grow up a little.