So one way to keep our minds and still eliminating segregated women and men sport is to segregate based on other attributes that correlate to an unfair advantage, just like those examples above.
However, until we do so, the problem remains that there are clearly advantages physically to being a man and that is why we have male and female sporting events. That distinction doesn't magically go away because someone does not identify with their gender. The division isn't about gender, it's about sex.
Those problems have remained for a very long time and yet we have done very little to remove those clear unfair advantages. What should we do until we fix them? I prefer common solution to similar issues so what ever fix that is deemed acceptable should be usable for all form of genetic advantages, and it would likely resolve a bunch of doping problems at the same time.