I've had this discussion before in the forums, but here goes nothing. Is a man that says he is a woman and immediately competes against them at an advantage - yes he is. Is a Transgender person, born in a mans body, goes through hormone replacement treatment for approximately two years and then competes at an advantage - pretty well no. By the time the hormones have reduced muscle mass to female levels there are no appreciable advantages. If there is any minor advantages it is not in strength, but things like slightly bigger hand sizes. Makes you better at catching a ball I suppose.
Should a man that says he is a woman be given instant access to a woman's change room? No. Should a Transwoman who has gone through about 3 - 6 months hormone treatment be allowed access - definitely. By this time she will have breasts, her genitalia will be useless, her testes will be sterile and her libido will have been reduced to nearly nothing. She would be way less of a risk to any woman in the change room, than the advances of a normal lesbian who still has her natural libido.
The real problem that this debate throws up is that we still have the majority of our community who cannot accept that the human race is not a binary system. Man/Woman is a religious idea that was first created in the old testament. Genetics show us that the human race is way more diverse than that. The Intersex community displays that trying to shoehorn people into gender boxes is stupid. The AIS girls even more so.
The good news is that sporting associations around the world have put an awful lot of thought into this issue. Hormone levels and time spent transitioning have been set as a benchmark to ensure a level playing field as much as possible. I trust the associations to get this one right. Lets face it - transgender people have been in existence for more than 40 years and they don't own all the female sporting records, do they?