The history of sex testing in elite sports is long, and even a cursory review of this history would demonstrate the erroneousness of statements like Lord Coe's and Rojo's. There has never been and will never be an easy answer to questions regarding the categories based on sex and gender in sport. Every attempt to find one has failed.
In the early twentieth century, female athletes were subjected to "naked parades" in which they had their genitals inspected by doctors to verify that they were in, fact, biologically female. How humiliating and degrading this was for the athletes needs no further explanation.
Chromosomal and hormonal tests are certainly less crude, but they have proved ineffective as well. Using these tests, athletes who have never once questioned their own femininity nor had it questioned by others were barred from competing. See Maria Patino for a famous example of an athlete who failed one of these "sex tests" and was later reinstated. Situations like this appear multiple times in the history of sex testing in sport, and this is because no single sex test could provide a complete picture of one's biological sex, let alone one's gender identity. For one's biological sex to be of any use in sport, we would need a complete picture of all the biological parameters that determine performance. Without this, any lines drawn are bound to be arbitrary and wrongfully exclude at some people.
As other posters have pointed out, Bolt did not run 9.58 simply because he has higher testosterone than any other male sprinter. Similarly, the only reason that I (a man who has never identified as anything but a man) cannot run 12:59 for 5000m is not because I have less testosterone than an elite runner. Certainly, testosterone plays a large role in performance, but it alone cannot explain why one person is faster than another, and why there is overlap between the running ability of the grand majority of men and women in the world. We would also need a complete picture of each athlete's full biological makeup, likely including physical inspection of their genitals as part of sex verification. Such surveillance would need to be consistent and long-term, as it already is with the rules for transgender athletes who wish to compete in the NCAA. Admittedly, most elite athletes would probably consent to such extensive monitoring and surveillance as they do with drug testing.
Perhaps these are the necessary evils to make elite-level sports entirely "fair." However, I think Lord Coe, Rojo, and others who think similarly should stop and think about what sort of sporting world they would create were they to apply the principles of their rigid, biologically-determined sex worldview consistently, thoroughly, and non-arbitrarily. It would be a sporting world in which the details of athletes' hormonal makeup--including fluctuations that occur with sex, pregnancy, and periods--are monitored and charted to ensure that no one with too much of the wrong thing is allowed to compete with other women. Of course, consistent application would also mean that the men are subjected to the same surveillance. I imagine many of you who might disagree with what I say in this post consider yourselves advocates of small government. You should keep in mind that the maintenance of a rigid gender binary, in sport and in society at large, requires rather intrusive measures on the part of governing bodies to ensure that there are no deviants.
If I were to talk about gender-identity and its social construction in this post, it'd be even longer than it already is, and it would become a conflict about fundamental world views. I can only say that I hope the history of sex testing in sports illuminates the fluidity and ambiguity of what makes a man a man and a woman a woman. I can also say, in regards to a related issue, that you should really stop and ask if these sorts of sex verification tests are the sort of thing we should subject young people who wish to compete in high school or college sports purely for the joy of it. It MAY be the case that it is "unfair" for young trans women to compete with cis women, but is that the most important thing about sports? Is excluding trans, intersex, and others who fit outside of the rigid gender binary worth what it may cost to their self-esteem and place in society?
-OklahomaGuy
P.S. some sources below. Rojo, as LetsRun is one of the most prominent voices in track and field, I think the responsible thing would be for you to read some of this history and other scholarly literature on the topic. I even think reading some social scientific and feminist critiques of the sex testing and the gender binary would be useful, even if only to help you develop your own viewpoint and counterarguments further