I disagree to an extent. There are sports that are segregated for no damn good reason at all. Like archery or figure skating or the balance beam in gymnastics and shit. A sport can and should regulate itself and determine if your sex gives you some kind of unfair advantage or not. When that trans swimmer won some events (though not all of them, she did lose some events) the governing swimming body ruled people who went through puberty as a male could not compete in swimming and sure. If there is a scientific reason backed by evidence, gotcha. Just banning everybody from considering anything is too heavy handed.
Sports is pretty fucking sexist man. Sure men have an advantage but people way overstate it and in many cases it seems counter productive. I mean the reason most of us play sports is to learn team work and other social values, not to win the Super Bowl someday. But how often outside of sports are we working in a gender segregated environment? Hardly ever. It seems more socially productive to encourage sports to be co-ed whenever reasonable. But that is another issue and besides, this whole trans sports thing really only impacts a tiny number of people. Hardly a big deal.
And I don't get the legal documentation at all. People can change their name, right? Why not their gender? What difference does it make? Besides if somebody is walking around being called a man's name and looking like a man in every respect it just creates confusion if then they are legally identified as a woman.