It’s not about gender identity. It’s about distinction in physical performance. A women’s category exists because the base level and top level of women’s physical performance is drastically lower than men’s physical performance. A transgender category could exist to separate transgender women from the women’s category given their physical advantage from being born male, while also separating them from the men’s category given their likely physical disadvantage due to HRT or other procedures.
Players can never be categorised by their identity, because if a transgender woman hasn’t (yet) had any procedures done, then her performance will be on par with men. Categories therefore have to be based on inherent physical capability.
While transgender men might also have some lingering disadvantage of being born female, it doesn’t matter as much, because they likely want to be seen as men and compete in the mens category regardless. This is not a problem, because they don’t have an unfair advantage. The problem arises when transgender women want to compete in the women’s category. The unfortunate consequence is that there isn’t a true place for transgender women in sports. They are too advantaged to play in the women’s, too disadvantaged to play in the men’s (and also they likely want to be seen as women and therefore wouldn’t want to compete with men anyway), and there is too few to create a separate category.
To have an open category instead of a mens is the best solution. By removing the “mens” label from the category transgender women (or anyone really) can hold on to their identity while competing fairly (even if at a disadvantage). Transgender men can compete even in the early stages of their transition without having to justify themselves. And women can challenge themselves if they deem the local or regional women’s category too weak. All the while women still have their own category that doesn’t include anyone who would have an unfair advantage based on inherent physicality.