I think the arguments for mixing the genders for sports is are very left brain. Like they always name all the positive benefits for the trans community like being able to feel less ostracized etc., and that in effect the vast majority of trans athletes would have nearly no effect on the outcome of sports because the numbers are so small. While I agree we the sentiment, we have different sports for classically defined men and women because of the generally different potential abilities of classicaly defined men and women.
It really is a fringe issue and the focus it gets as one of the conservative party's main issues is kind of silly.