If you read the very first line of the first comment I made above [0] you'll see why the "but some are better than others" is a very unrealistic and uncharitable take on the topic. The whole reason we have separated men and women trials in almost every sport is that the difference between men and women goes far beyond "lots of athletes have an advantage over each other". Having a male body for 35 years is much more than your average advantage.
You decided let your personal sensibilities get in the way of understanding my arguments that are much stronger than anything you presented. Sports aren't about gender identity but about sex. As entitled as any individual is to decide on a body that reflects their identity, their biological sex is still very much unchanged. And so are the advantages years of being a male provide.
As you can see from actual athletes, this situation is offensive for those women who after a lifetime of training and hard work see themselves competing against effectively a biological male body with a massive advantage that dwarfs even years of performance enhancing drugs would give.
And to your last point, saying gender identity is OK, age identity is not [1], and that it's OK to identify as a different gender or even no gender at all but anything else is not acceptable is grossly hypocritical and might be as ignorant as people were 50 years ago about gender related topics. Time will tell. I honestly do not feel like my age, and do not identify with that number but rather with a much younger age for many of the reasons you can read in the article linked. This being said, even if the law allowed me to change the number either way, I would not consider this to be a valid differentiator for sports.
[0] https://news.ycombinator.com/item?id=27603055
[1] https://www.theguardian.com/world/2018/nov/08/dutch-man-69-s...