> There's a "human being" class, and a "human beings without the testosterone gene" class. The only reason to have the second class is because only half of the human population has the "testosterone" gene (aka the Y chromosome), and the other half still like to run.
While it's always cute when people pretend that human sex is simple and things only get complicated when gender identity is considered, chromosomes aren't genes, the Y chromosome isn't the “testosterone gene”, XY females exist, XY females with a normal copy of sex-determining region Y (SRY) exist, and, as was discovered recently, XY females with a normal copy of SRY who have borne children exist. Also XX females have testosterone at various levels.
It's true that recently was part of how to deal with the evolving understanding of gender in the context of sport, a number of governing bodies have redefined the criteria for competing as a woman to be based on a combination of identity and serum testosterone levels, but that's also not about a “testosterone gene” and at best imperfectly correlates with any particular gene.