Trans women do not belong in womens sports as they are not women. That's not transphobic, it's a fact. They should never be allowed to compete in womens sports. The biological makeup should determine the category they compete in, and his would be male.
Although I have said I am unconvinced that women can't compete against transwomen, I have also seen that there are a lot of passionate people who believe that it's unfair to have transwomen and women in the same category. I thought of a possible solution today.
In terms of respecting trans women who wish to identify and live as women, I think instead of having "female" and "male" categories in sport, there could simply be a "universal" category along with a separate "female" category.
The "universal" category would allow anyone to compete... male, female, disabled, transgender women, transgender men, etc., etc. Given that men generally achieve the best results (regardless of the cause), in practice, this category would likely be dominated by men (which is fine, because this category is effectively replacing the men-only category).
The "women only" category could continue to exist, without any transgender women or transgender men, with the justification being that it promotes female participation in sport.