I am transgender and this is hard topic to "get right." I can see where both sides are coming and right now I can't side with either. They both have valid points and contentions. Basically, we don't have the right answer right now and it it needs more study to understand. There is a legitimate reason why there are male and female sports as there are distinct differences in how males and females develop.
Having a transgender person creates contention and in reality even being on hormones doesn't solve all the problem. There are some studies saying after starting hormone treatment tends to reduce muscle mass similar to the opposite gender. However, that does not take into account the bone structure, the developed heart, lungs or over physical size. On the flip side, there are women who produce more testosterone naturally who tend to have masculine traits.
Basically, what I am saying is it very muddy and I don't know if there will be a right answer. I believe in being fair and respectful.