Gender is a social construct - but that doesn't mean it's not real. Many people, a majority even, identify as either male or female (for whatever reason they think is right for them).
What the whole trans sports debate is about is trying to do is define a line of physical difference - i.e. sex, not gender. And what scientists are finding in this regard is not that there are no differences, but that even sex is a very fluid system.
Chromosomes have a few distinct states (more than two) but that's not the only factor determining sex. Hormone levels could be categorized as above or below typical values (i.e. the current official measure) but even that is not the end-all determining factor and completely leaves other factors like ethnicity (see Caster Semenya) out of the picture.
What they recently have been trying to do is find another measure that more reliably correlates with physical attributes like strength, endurance, etc... and that's a lot more complicated than they had hoped. It's mostly a problem of a few exceptions to whatever rule they think they've found. For well over 99.9% of athletes all the rules come to the same conclusion of what category to put them in.
I will not talk about whether it makes sense to put athletes in separate categories or how many of them there should be or the difference between amateur and professional sports. That is a choice you'll have to make for yourself. All the sources are out there.
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