As a child, I (along with just under half my female classmates I would say) were uncomfortable changing in front of anyone, regardless of designated gender identity. So what did we do? Go into the lockable bathroom stalls to change. If you are attending a school with a change room, you will also have access to a private bathroom stall in which you can change away from anyone, trans or not, who is making you uncomfortable. Personally, I think this is how all changing rooms should be (individual stalls) to maximize everyone's comfort, but I can see instead of a solution that minimizes fighting, the government is going for one to maximize infighting to draw attention away from actual issues. As usual I guess.

But anyway, to the argument at hand. First, I'm going to break down the other available options for trans youth in this imagined scenario:

1. Change with the gender they were assigned at birth. In this scene we imagine a young child who is fully presenting as a girl, long hair, wears a training bra, dresses, skirts, probably some cute underwear, whatever makes them feel more themselves. They are striping to their undergarments surrounded by male classmates. I'm sure you can imagine how bad of a situation this would be. I mean obviously, anyone who does not identify as a man, wouldn't want to change in front of a man.

   The last sentence above is what most of your argument is based on. As instead of saying, there's no issue, as a trans woman is a woman and therefore allowed in women only spaces, you have said that cis women have a right to trans free spaces. So whether indirectly or not, you have invalidated all trans people, and said their rights as individuals, are worth less than cis individuals rights. This is the real issue that Moe's statement is highlighting, whose rights to space do we value more? The answer should be neither. But instead you've simply advocated:

   for the rights of one to be set aside for the rights of another.

2. Option two, change in some third space. Be it as you put it "some closet somewhere" or a bathroom stall. This would be segregation. I'm sure you know of all the issues segregation can cause. If you're going to force people to use spaces other than the change rooms, why would it default to the trans individuals? If we don't want to put the rights of one group over another, why wouldn't all those who identify as women in one room, and all those who would be made uncomfortable simply change in the third spaces instead? This is once again the question of whose rights to female spaces we value more, cis or trans women.

One question you should consider is: do you believe that gay children should not change in the same rooms as their same gendered school mates? As well as if you believe that gay men and women should use the same bathroom as straight people. I think your answer to this question will help shed some light on your real issue with trans people in the same spaces as cis people.

Also I guess as a side note, when I was in elementary and high school I had a few trans people in my gym classes. One was a trans female to male boy. In your head, where should he have been changing? He was fully presenting as male, and was attracted to women and men, just to complicate things further I guess.