While there may be some advantage, I'm not aware of any sports on any level where transgendered women are the top-level athletes. If anything, they are under-represented in the top levels.
So, do you feel these "certain advantages" necessitate discrimination?
In 2017 and 2018, Terry Miller, a trans woman,
won the Connecticut women’s high school track championships in the 55-meter, 100-meter, 200-meter and 300-meter events. Her closest and only real competitor those two years was
Andraya Yearwood, who is also a trans woman, so now you are aware that it actually happens.
The Williams Institute at UCLA states the U.S. has 1.4M transgendered people out of 329MM total, or .4% of the population. Of that, only a small portion will be "athletes", and even a smaller number of those will be in the peak age group. It is a small number, so you would not expect to see many period. I'm not sure such a small percentage can be underrepresented.
Sports between men and women were separated for a number of reasons, where in our history, modern sports for women started out for high class individuals, with "feminine sports". And physiological differences between the sexes has been the key driver to keep most sports separate.
For me, we shouldn't judge if someone gets the podium as a litmus test. A genetic female, may miss out on a qualifier or the olympics to a genetic male, or perhaps a scholarship or even a spot on the team. It is foolish to believe that this isn't happening and/or won't happen.
If we combined sports men would take the top spots, scholarships, etc. in the majority of sports. Allowing a genetic male to participate in women sports is just a smaller effect of the same thing. Do you disagree?
Separating athletes by biological sex is necessary because the gap between the best male and female athletes – at all levels – is dramatic.
I'm very sympathetic to transgendered people, and honestly feel for what they are dealing with. If you are born male and believe you are female (or vice versa), no amount of surgery, hormones, societal acceptance, etc., will ever make you whole. You were still born in a body that conflicts with your brain. No matter how supported, the suicide rate for transgendered people is astronomically higher than cisgendered people. As a society, we have to decide what the role of government/society is in protecting the rights of individuals when the rights of some other people appear to conflict with those rights. Many cisgendered female athletes are the biggest proponents for keeping transgendered women out of their sport as they believe it is inherently unfair.
That is the situation we see happening when young females are beaten in sporting events by a transgender female with increased, unfair advantage. This promotion of equality turns into inequality for others. The impact will increase the more it is allowed.
I think we should have Open divisions and women's divisions. Anyone can compete in open divisions, and genetic women can compete in the women only divisions.