I think there are differences between gender and sex. A transgender woman is a woman gender-wise, cause they identify themselves with the woman gender, it is a social construct, and we must respect that. Someone who doesn't respect the need of others to be as they want and like, when that someone is not impacting anyone's right to be free and not doing any damage to anyone, had some psychological problems themselves (see a therapist, really!).
But the sex to whom they were born was male, and males and females (sex), have many differences not only testosterone, like bone structure that permits them (males) to run faster and be stronger and them (females) to give birth.
We are an evolved civilization, and we should not discriminate against someone who has a difficult life, borning in the wrong body, feeling different, defective, unloved, and full of shame. Increasing their suffering! But are we doing the contrary by allowing them to participate advantageously in the woman (sex) category? And should female born females (sex) that had dedicated their lives to a sport be at a disadvantage cause another woman (gender) has not been born a woman (sex)?
So this is a dilemma, a big one, I sympathize a lot with the suffering of trans persons and want it to be the lowest possible (I'm a psychologist BTW and I have some trans clients), The problem is I don´t think it would be less discriminative what a woman (gender) would listen if they start dominating something like tennis, in fact, I think that woman would be in a lot of suffering and will feel completely unaccepted, unloved, defective being paradoxically worse to them being accepted as a woman (sex) in that sport.
To be a trans woman (gender) is not the same as being born a woman (sex), unfortunately.
And I think weighing the pros and cons that they (trans women) should get a distinctive category to for them to compete (even to protect them). Many people say there isn´t an advantage, but we are clearly seeing some trans women winning competitions in different sports, and then there are still to happen a trans man to win any male competitions, is not this a sign that there is an underlining advantage to be born a man (sex) competing in woman (sex) category?