Your assertion that hundreds of millions of women support transwomen in female sports is categorically incorrect.
There is plenty of data.
According to a 2023
joint statement by scientists, "in athletic events and sports relying on endurance, muscle strength, speed, and power, men typically outperform women because of fundamental sex differences dictated by their sex chromosomes and sex hormones at puberty, in particular, testosterone."
The Biological Basis of Sex Differences in Athletic Performance: Consensus Statement for the American College of Sports Medicine
If they undergo
hormone therapy as part of gender-affirming measures, the differences to cisgender women are reduced. But even then, there are still advantages.
Mayo Clinic: Feminizing hormone therapy
British Journal of Sports Medicine, the absolute hand grip strength of the 23 participating trans athletes (after at least one year of hormone therapy) was higher than that of the 21 participating cis women.
"Trans women as a population group are taller, bigger, and in an absolute sense stronger than cis women," explained Joanna Harper, a medical physicist at Loughborough University in the UK.
Effect of gender affirming hormones on athletic performance in transwomen and transmen: implications for sporting organisations and legislators
A
2020 study by Timothy Roberts and colleagues at the University of Missouri-Kansas City examined US military personnel who underwent gender-affirming hormone therapy.
In 2021, Alun Williams and other researchers from the British Association of Sport and Exercise Sciences
came to the conclusion
After one year of hormone therapy, trans women performed better in sports than cis women.
A 2022 study of 228 trans women in the US Air Force found that they had had worse performance in push-ups compared with cisgender men, but with little difference in sit-ups or run times, before starting hormone therapy.
The trans women performed significantly better than cisgender women after one year of hormone therapy.
Effect of Gender Affirming Hormone Therapy on Athletic Performance: A Four Year Follow Up Study