I always think it's very helpful in these discussions to compare and contrast trans women and trans men, using Lia Thomas and Iszac Henig as an case study.
Lia Thomas competed in the men's swimming for the University of Pennsylvania, ranking no. 462 (I believe). Thomas then decided to transition, and after a year of testosterone suppression, was cleared to compete in the women's events. Thomas then started winning races (in one case by as much as 38 seconds).
Competing in the same events was a trans man named Iszac Henig. Henig has had a double mastectomy but was not taking testosterone because testosterone is a performance enhancing substance and would have disqualified him from competing in any category, whether the women's or the men's. He was vocal about the fact that he thought trans men should be allowed to take testosterone and compete in men's categories, but accepted that this was not allowed and decided not to take testosterone and to compete in the women's categories. In one race Thomas finished in first place and Henig finished in second place.
Aside from the competitive advantage issue, Thomas insisted on using the women's locker rooms. Competition swimsuits are incredibly tight. Getting into or out of one involves a lot of very undignified contorting and can take as long as 15 minutes. It's not the kind of thing you can quickly whip on and off whilst hiding under a towel, so basically the female swimmers had to be OK with being completely naked in front of each other. They were not comfortable being naked around Thomas, who has male genitalia and is attracted to women, in their showers and locker rooms. But when they complained, their concerns were dismissed. They were told to put up with it or be kicked off the team.
Riley Gaines, a University of Kentucky swimmer who completed against Thomas, has been extremely vocal in her activism on this issue. She has been smeared, discredited, threatened, even assaulted on more than one occasion. All for daring to speak up and say, "This isn't right."
Back to the testosterone point. The rules which have typically allowed trans women to compete in women's categories in the past require the person concerned to reduce their serum testosterone levels to less than 10 nanomoles for a period of at least six months prior to competing. No female person has a testosterone level in this range. The normal range for a woman is around 0.5-2 nanomoles. The reason this threshold was chosen is because it is a threshold which takes the person out of the range for a normal male, and can be achieved by testosterone suppression. It is, however, five to ten times higher than the range for a normal female. It is also far higher than a female can achieve even by doping.
Which brings us back to trans men. If someone like Iszac Henig took testosterone as part of his gender affirming care, he would not be able to achieve a testosterone level equivalent to that of a natal male. So why should he not be allowed to do this and try out for men's events?
The point of the anti doping rules is to prevent athletes from using performance enhancing substances to obtain an unfair advantage. This is why a trans man who has taken testosterone obviously cannot compete against women. But why should they not compete against men? Their testosterone level is still going to be far lower than the men. They have not gone through male puberty. There is no unfair advantage. Even with testosterone, they are unlikely to qualify in men's events at all.
And yet Lia Thomas was allowed to compete as a woman under the influence of the same hormone that would disqualify Iszac Henig from competing. Not only the same hormone, but a higher level of it. But because that hormone was produced naturally, by Thomas' testes, rather than injected directly into the bloodstream, and because Thomas had made efforts to reduce it, the competitive advantage was deemed not to matter.
When you look at sport, it's as clear as day.
Heads male people win, tails female people lose.
And this principle can be extrapolated to most, if not all consequences of allowing people to identify as the opposite sex. Whatever the issue is, the impact of it is negative for people who were born female, and positive or neutral for people who were born male.