Sex does play a role in how we interact in public. I don't want men in a public bathroom with me or in the shower. Or competing against me because he said he's a woman at the age of 19.

Agreed, they are women because they identify as women.

Not how it works, I explained that to you already. You can't identify as something you aren't. Every cell in your body has XX or XY on birth, by saying one thing one day, and the next the other day, doesn't change that, nor does it change your muscle or bone density.

The vast majority of women are not American. Yet Americans can still be women.

You're funny :D

Hell some women have XY chromosomes. This is a fact, and it would be improper to say “all women have two X chromosomes”

And that's a medical abnormality which we call intersex. Here's a fun fact: Conditions in which chromosomal sex is inconsistent with phenotypic sex, or in which the phenotype is not classifiable as either male or female, occur in 0.018% of the population [1].

It's a bad faith argument to say women can be men and vice versa, but you have no issue with that.

Would you change your mind if a study showed that trans women who undergo hormone therapy that suppresses their testosterone levels sufficiently do not retain an advantage over cis women?

I wouldn't - The general structure of the female pelvis is thinner and less dense, in comparison to the thick and heavy male pelvis, which is designed to support a heavier body build.

This gives men, with a bunch of other things as muscle distribution and density a major advantage in a sport such as running. No amount of drugs can stop the development of that, and they will always be quicker than me.