On trans female athletes, it's complicated. On the one hand the idea of acceptance as a woman is very important for them, and that means inclusion in female-only activities or spaces. On the other hand there are going to be clear and undeniable physical advantages for those born and who develop into an adult male elite athletic form before transitioning. Sometimes those who see inclusion as being more important than fairness/parity in sports (which in a vacuum should be everyone) can sometimes try to ignore or downplay this clear advantage. While one is more important than the other it doesn't discount the clear problem with competitive advantage you're going to have with male-sized bodies in female competitions. If you care about sports (and many do) something will probably have to be done to address this.
On the other hand, the issue is a small one in the overall trans acceptance issue. Most folks over a certain age have trouble wrapping their head around it, myself included, even if they accept it. 20-30 years ago I'd wager most people in this country hadn't heard of it, let alone had an opinion on it. Also 20-30 years ago the idea of gay marriage was one the public was firmly against. So that gives me some hope on this issue. But an issue like the trans athletes controversy is a block in the road because it allows those who are against trans anything to point to it and say, "see, this is going to be a problem!" And those who are confused about the idea of a man being born in a woman's body or vice versa are a lot less confused about the chances of a transitioned Lebron James being able to effortlessly outcompete even the greatest WNBA stars (who, gun to my head and most others, we could not name).
I have no doubt that's why this narrative is being pushed, it serves an anti-trans agenda. The problem is, there's a point here (even if it's being hijacked to suppress the rights of a group of disadvantaged people). So it should be addressed.