I think the root of the problem is the strict categorisation of people into boys & girls, men and women, when they are primarily human beings with far more in common than otherwise. Even now in 2020 we still have schools with a Boys entrance and a Girls entrance, different uniforms, separate Gym and sports. From an early age there is boys/girls clothing, toys, expectations, books, comics. There are Gender based names for occupations, eg Postman/ Postwoman, Head Master, Headmistress. etc. (In Scotland we tend to refer to these as the Postie and the Headie, both Gender neutral terms.
As to sports, there are many where gender, weight, height are irrelevant (thinking of Archery, Yachting, snooker, bowling, etc. where skill and expertise matter most) Boxers are divided into categories from Heavyweight to Bantam weight, so that the contest is equalised. In Golf at club level, people have handicaps to allow them to compete on equal terms. Why can other sports not grade people according to their size, strength, etc? This would be a bonus for small men as well as women.
It seems that most of the objections to Trans women are based on changing rooms and toilets - a dilemma which would be easily solved by having all such facilities unisex with cubicles, including sink and sanitiser, for all. As a denture wearer I would love this privacy
If we could eradicate the unnecessary divisions by gender and concentrate on treating people as individuals, free to adopt their own life style, eg clothing, activities, sexual preferences, occupations, etc. then people would blossom, free from being forced into a straight-jacket not of their choosing.