How people understand the word "woman" may differ from person to person, group to group or even society to society; but that womanhood exists as an objective quality, regardless of what we think about it, is something most people would not disagree with.

So, since there is an unresolvable (rationally) division between objective reality and subjective perception, how do we deal with conflicting notions of womanhood within a free society?

It can only be a matter of what a critical mass of the society's members acknowledge womanhood to be. For example, almost no one would disagree with the statement that Kate Hudson is a woman; therefore, it makes no collective sense to bar Kate Hudson from safe spaces created for women. However, there is substantial disagreement with the statement that I, a transgender female, am a woman; therefore, it does make collective sense to bar me from safe spaces created for women. Do I like this? Absolutely not. But this is the only way a free society can define womanhood.

This is why the fight for "trans rights" will ultimately fail. The fight for rights as victims of gender dysphoria will win, because gender dysphoria is something we can prove; but we cannot prove that "trans women are women." That is something most trans women, myself included, believe to be true; but it is just that: a belief. And, in a free society, we do not make laws based on beliefs.