I'm of two minds on this.
1. I agree that trans women are not women and that it's unfair for them to compete against biological women. I have nothing against trans people, but let's be honest, they are in a unique gender category.
2. All people deserve equal treatment and dignity. Many trans people identify as the opposite of their biological gender. Like all people, they want their identity acknowledged and respected. If they happen to be athletes, a part of that acknowledgment and respect comes from competing as their non-bio gender.
I agree that you have to treat people who feel like they are not what their biological gender is with respect.
At the same time, you have to balance their needs with the needs of the society.
When a dude, says, "I'm not a dude!" society should say okay.
When s/he says, "I want to compete against girls!" we need to say "Well, you might feel like a girl, but your biology gives you a physical advantage over biological girls who feel like girls, so maybe, we need to balance your desires and feelings and biology with the desires and feelings of the majority in the society."
And the transgender girl, if she is cool, should say, "Okay."
It's actually a really good narcissist test.
I've had transgender students who are cool and it's super easy to accommodate them.
Then I've had some that use it to assert.