Holy crap... ok, i'm going to give my two cents if anyone is still up for somewhat civilized discussion... it's a very important question.
Personally, I don't care if the kid is transgendered or not but two things come to mind for me:
1) I don't think they created a girls league simply to segregate the sexes, rather it was accepted that due to genetics, men/boys typically have physical advantages over women/girls - and as such, they wanted to have a league where women/girls could find fair and challenging competition - the game is much more fun when it's a level playing field. Ultimately, if you're playing a sport, you should be playing in a league and with teammates where you are able to compete on relatively the same level so you're challenged. Boy or girl, if you're completely dominating everybody, it's not doing you, nor anybody else any favors and most players who want to be the best will simply play up or in another league. For girls, especially in smaller towns, that may mean playing on a boys team and most of us wouldn't have an issue with that - in fact, we'd applaud her. I think from reading the posts, this is the primary concern - that a player with the genetic makeup of a boy would naturally have an unfair advantage over the rest of the girls. I guess my view is, well, if this player who is a biological male truly is playing at the same competitive level as the other girls in that league, by all means go for it - transgendered or not. That said, if they are completely dominating or are obviously at an unfair advantage, like what we've seen in wrestling - it truly undermines the integrity of "fair" competition and again, really does the kid no favors - they should find/play/wrestle in a class/league that would be challenging for them. In soccer, that could mean the transgender kid could play up or with their biological gender - like any other girl/boy who was outplaying the rest of their teammates and league.
At the highest levels, this method does break down a bit because we all know that there are teams/countries out there who would be more than willing to take advantage of this to win - for example, what if Russia decides to bring on a whole team of transgendered players into the women's competition? In theory, if it's allowed, that could completely change the game and could possibly completely ruin it for genetic females to have an opportunity to play if the rest of the world followed suit. Which is why I think at that level, they probably should enforce genetic gender and brings me to point #2.
2) In regards to sensitivity towards the player - well, this is a tough one, but my perspective is the world cannot revolve around one person, nor minority (and I say this as a minority). Everyone has their issues and things they're struggling with. The same kid who's dealing with transgender issues may have a teammate or opponent who's dealing with something else - and they could completely conflict. You really can't expect everyone to cater to your kid's needs. Life is tough. Just because my kid is allergic to peanut butter, I can't expect every other kid in school to give up eating PB&J sandwiches... Yes, my kid could die. But it is a gross overstep in someone else's freedom to pursue their happiness and well, my kid needs to find a way to accept and survive with his condition. Allowing a transgendered kid to play in a league where he/she is dominating other players may bolster his/her confidence, but at the same time can be discouraging to numerous other players he/she competes against and ruin the game for them. If you stick with #1, I think most people would not have as much issue with it.
Anyhow, those are my thoughts... feel free to flame away... =)