... More like in the last 150 years since "patriarchy" was established in some countries.
Also, no transman ever won anything in any "male" sport.(AFAIK)
TLDR: Drawing attention of the "masses" we draw unwanted attention. You want to win Olympics? Good for you! Do it in your assigned at birth gender and transition afterwards! Caitlyn Jenner transitioned after finishing her sports career. Was noticed only for being part of the TV show! General population will always oppose ones who make waves! Move to the next city, transition on the way, 99.9% of the population will never know you had transitioned! (yes, you will need to put some effort into gaining a female voice...)

!) Yes. In some areas. As in sports. If a person was not on blockers and hormones since 5 years old, male will beat a female almost in any sport. Just because some of the bone structure that makes a bigger lever for the muscles is set, in some cases, when child is 6 years old. First great testosterone surge in boys happens between 6 and 7 years usually... That is one of the reasons why boys are most terrible at that age. Remember 150 years ago? 12 year old boy was considered a grown man in many cultures (including UK and US).
So, all of the phantasies where boy at 12 years comes to play for the girls team - are true. Average boy will give huge unfair advantage!

So... The problem... Too much attention drawn to the "problem". 300 years ago if you shaved closely (face only) and donned a woman's dress - you were a woman! If you had somehow tried to minimize your G-cups and donned a male dress - you were a male.

Remember "oppressive" "terrible" USSR? Remember what was done to anyone transgendered? Yes. It was what many of us dream now. Go to the local passport authority in dress and makeup with a passport size photo in dress and makeup, provide a proof of paying a passport reissuing fee (under 5 dollars at the USSR rate), receive a passport with "F" in gender square!

If you were not content with living as a girl with an "outie" and without natural breasts - there were additional hoops to jump.

Oh... Birth certificate that everybody seems obsessed about... "In soviet Russia" it is needed typically three times in a life of an average person:
When you get enrolled in preschool/kindergarten, when you enrolled to the school (usually goes without birth certificate as you transfer from preschool to school), when you apply for your passport at 14 (currently, or at 16 when i was a teenager). Yes, there could be additional occurrences of the birth certificate use if parents are divorced before preschool... But it happens not that often.

"What is a Woman?"
As soon as we will figure it out - they will change the definition!
I am a woman... somewhere in my outlook, how I can "do" woman's logics, how my woman's intuition works in some cases. (It is not easy to be a lesbian when you look like obese old guy ;-) ) But... As soon as girls around start to suspect that I understand their logics or intuition - something changes... And, go "à la case départ". You have to decipher their logics from square one... ;-)