This is something that is not well studied because the population of study participants couldn't really be too large, but there are studies. Neither side of the argument will really like the results because they're incredibly nuanced.
The only thing you can really say with certainty is people who think a transgender woman (someone born male) definitely has an advantage over cisgender women are wrong. People who say a transgender woman definitely does not have an advantage over cisgender women are also wrong. 99.999% of the people arguing on either side of this argument isn't knowledgeable enough on the topic to be so certain in their opinion. That includes the politicians on both sides of the aisle.
The data shows it all depends on what type of athleticism we're talking about and how long after transition that athleticism is being assessed.
Here is one of the few comprehensive studies, but it really only looks at pushups, pull ups, and 1.5 mile running times. After two years of hormone treatment there is zero statistical significance between the 1.5 mile times of transgender women when compared to cisgender women. After four years there was zero statistical significance in the maximum number of pushups and a very slight difference in the maximum number of pull ups.
A single study does not prove anything. It's an area that requires a lot more research but unfortunately that research is hard to come by.
Bottom line, the people who say "Obviously a man [referring to a transgender women] would have an advantage over women" are wrong. The people who say "There are obviously no differences between the two" are also wrong.
The comment was about trans women who never experienced a biological puberty.
We don’t need a great scientific study to know that bone density, lung volumes, size, and muscle development are distinct between men and women. And, the anecdotal evidence in competition is dramatic. For example, Lia went from about 400 ranked in men to the top of women swimming. Could Lia maintain that status with years of treatments, rather than the short duration required at the time for competition? Don’t know.
But records falling in women’s sports by self-identifying men are real evidence. Not just a coincidence.