I'm in agreement with all of this.
And incidentally - as I've stated before - I also believe that those competitive sports* in which anatomy and/or physiology play a competitive factor** should be sex-segregated. I know that this is not Boudicca90's position, though I'm not sure whether or not there's any difference of opinion on this matter within either the transgender community or those lobbying for transgender rights. I do however believe it very highly likely that the bodies administering all of the relevant sports will - sooner or later - instigate measures to exclude transgender competitors.
* Though only for mid-level (eg local region, state) and high-level (national, international) sports - outside of these levels of competion, I believe transgender people should be encouraged to compete in sports with their trans gender, and that they should be welcomed and accepted for it.
** As I've already argued: I believe it to be obvious that someone who has, for example, gone through childhood and adolescence as a cis male has already developed, on average, a comparatively advantageous (compared with female cis women) anatomy - bone size, bone strength, bone density - and physiology - heart size and strength, lung size and strength, muscle mass/nature/strength). And none of these biological areas of competitive advantage will be significantly altered by any form of gender transition.
I apologize, because this is going to be long. Bear with me.
I'll start off with saying that for young children (perhaps until near puberty) there is no reason to segregate at all as their physical development at that point doesn't bring too many issues.
My daughter didn't start sports until 7th grade (age 12 for those outside the US). She started Volleyball and softball at that time. She played two years of Volleyball in middle school, three years of park district softball, two years of high school (Sophomore and Junior), and two years of club softball (Graduated as a Junior). She also did two years of competitive cheer-leading (Freshman and sophomore years).
Now, the star player on her 7th and 8th grade volleyball teams was a girl who was taller than the rest. She also played basketball and went on to play for Ohio State in college. In junior high, I'm pretty sure she would have outplayed anyone on the boys team. At that point she had an advantage in height and strength. But by high school, those same boys had overtaken her. She would not have made the men's basketball team at either high school in town.
But she was considered the top female basketball player in the area and one of the top players in the state.
High school sports are not low level social activities. They are very serious and they are what feed into the high level sports in college and the pros.
Similarly, if softball were not sex segregated, neither my daughter nor any other player on her team (several of whom played in college) would have made the high school team. The next thirteen boys who didn't make the cut for baseball would have. (The sports are different, but similar enough to cross over.) This is all in the age range of 14-18.
It's not just the batting. When my daughter was 18, I watched one of her then boyfriends slow pitch games. This was essentially a beer league with guys of, shall we say, questionable fitness. My daughter was an excellent fielder with great wheels. But these guys playing casually had speed in the outfield that ran circles around the fasted of the girls even in the higher level travel teams I saw. Their skills left something to be desired, but physically...no contest.
My point is that the advantage is HUGE between males and females. In principle I have no problem with a trans-woman competing with the girls, but I think the parity/lack of advantage needs to be demonstrated, preferable in individual case judgements by the various leagues. I don't think a one size fit all standard is fair to anyone, but it sure is easier to write into a rule.
Also, around here, volleyball is huge. For girls. There are no boys' clubs male teams in high school or nearby universities. But there was a boy who wanted to play. So the prominent local club took him and made an agreement with the other clubs with some conditions on how he could play. He could only play back row, where his advantages were lesser (height is less desirable in the back row) and I think he could not play libero. It's wasn't a transgender situation, but it's an example of an accommodation made for an individual case.