So we all need to get what? Blood tests? Carry around proof that we are all women?
We have show proof all the time for various reasons. We have to provide proof of our age, address, right to work, qualifications, driving licences, all sorts of things and have done for years.
If it keeps males out of female single sex spaces, services, sports, sponsorships, grants, awards, prisons, shelters, hospital wards etc. then I don't see the problem.