"Firstly, it’s essential to debunk the ... inherent and insurmountable advantage over cisgender women in sports."

Well, it’s hard to debunk fact. :-) And you don't.

Yes, it's quite true that individual physical characteristics, applied generally across entire populations, show bimodal distributions when comparing men and women. A female track star will definitely outrun a 90 year old man. :-)

But, athletic competitions are not competed across broad populations; they are competed across relatively specific cohorts which become more specific as one approaches the elite (98th percentile and up) competitive level.

So, when you compare the actual competitive cohorts (men performing at the, say, 70th percentile level for men against women performing at the 70th percentile for women) there is no bimodal distribution. The men clearly and unambiguously outperform the women by substantial (in track and swimming, it's between 10 and 15%, in some sports as much as 50%) margins.

Now, as you point out, that's influenced by a number of factors, but by far the predominate factor is MALE PUBERTY. All of us who have competed (myself, swimming) at a high level have seen this happen in real time.

When we are 10 years old, the "fast lane" during practice consists of the fastest boys and the fastest girls. The differential between male and female at that age is about 1% in favor of the boys. So, it's mixed.

Then, as we aged up, we (the girls) got "demoted" out of the "fast lane", because suddenly the boys who we used to beat easily suddenly.....were faster than we were. And by the time we aged into the 15-17 age group, we girls were in the middle of the pool, with the fastest two lanes being all boys.

Now, we were still great; we were winning our meets and were faster than all the other girls on other teams at swim meets, but the boys were substantially faster by virtue of puberty.

Same training, Same coaches. Same nutrition. Same mental preparation. What was different? The influx of testosterone that they got and we didn't.

"Moreover, trans women who undergo hormone therapy experience changes in muscle mass, strength, and other physical characteristics. As testosterone levels decrease and estrogen levels increase, the playing field becomes more level."

Right. MORE level. But never LEVEL. This is at the center of research right now. BUT, there is a basic error being made, assuming as you do that the difference between performance is musculature only. I will explain:

HRT, for the most part, affects muscle strength only. But males have other physiologic advantages that females don't. They're taller, and height (and limb length) impart athletic advantage. The geometry of the shoulder joint is different; men can generate a LOT more power than women can due to physics. The shape of the pelvis is different; because of this, men can generate a lot more speed and power in the lower torso than women. Again, physics.

HRT affects none of this. Men also have advantages in their cardiovascular and respiratory systems that HRT only alters in a minor way.

But, back to those studies on musculature. The current and evolving consensus is that HRT can abrogate male puberty and musculature advantage after 7-10 years, which is far longer than the guidelines in earlier regulations. Because of this, both World Athletics (track and field) and World Swimming, in just the last year, updated their guidelines which, for all practical purposes, eliminates anyone who has passed through male puberty from international competition.

Bottom line here is that there is no known way to alter male physiology sufficiently to so impair the male to make competition in the female category fair.

"Many sports governing bodies, like the International Olympic Committee (IOC), have recognized this and established guidelines that require trans women to maintain testosterone levels below a certain threshold for a specific period before they can compete in the women’s category."

Again, it's not all about testosterone.

Also, the IOC has punted qualification decisions to the individual federations. (Most involved in this sporting debate consider this an act of cowardice, but I digress.) So, in the next Olympics, there will not be any "IOC guidelines"; it's up to the individual sporting federations to decide what their qualification regulations are. Two of the three largest Olympic sports have therefore said "No" to trans competitors; the third, Gymnastics, really isn’t involved in the issue because males and females don't compete on the same devices.

"A 2021 study published in the British Journal of Sports Medicine analyzed the performance of transgender athletes in various sports and found no consistent evidence to suggest that trans women possess a competitive advantage over their cisgender counterparts."

There are also plenty of studies (start with Hilton and Lundberg) that show the opposite. Best to let the readers search out the data and decide for themselves. But even the study you seem to reference (you omitted the link) doesn’t come to the conclusion you say it does.

"Sports should be an arena where all individuals are welcomed and celebrated for their dedication, hard work, and determination."

Not at the elite level. People can allow whoever they like into beer leagues, but elite sports has always been about the achievement of excellence. There are tons of athletes who work just as hard, are just as dedicated, and just as determined as Olympic qualifiers, and don't make the cut. We respect them but we do not celebrate them in those elite competitions.

"It’s also important to recognize that gender is not a binary concept."

True, but sporting categories are about sex, not gender.

"Finally, it’s worth noting that sports have historically been a powerful force for social change."

Yep. But social change can't trump fairness. If social change occurs within those categories, that's great. But putting social change on a higher plateau than fairness destroys the entire purpose of sport.