In May 2011, a budding movement at Oxford seems to have started at Green Templeton College and from there was picked up by Queens College and Trinity.
The idea seems to be that if a meeting is specified for "women" or "men", anyone can attend if they identify themselves as the appropriate gender. So wearing a dress would not disqualify someone from claiming he-she was a man. Similarly, I would guess that by the same reasoning someone with a mustache or beard, or both, could self-declare as a woman and attend a meeting for women.
In the United States, the question of exclusion by gender has played a great part in the history of elections and clubs and businesses.
For example, in 1848 when Elizabeth Cady Stanton was visited by her old friend Lucretia Mott and they reminisced about their exclusion from voting at the London abolitionist convention in 1840, they decided to have a meeting that weekend about women's rights. The first day was for "women only" and on the second day the convention was genderless. However, several men attended. It is not recorded whether they gained entrance by announcing that they were women.
One of the men who attended played a great part in the proceedings. The only black person in the group, Frederick Douglass, argued strongly that the women should claim the vote as their right. - rfr the same reason, he said, that black people were doing so - in order to advance their position in society.
Here is the resolution passed in May 2011 by the Trinity JCR:
Trinity passed the following motion at the JCR general meeting this evening:
This JCR will support the aim of the Genderless campaign for gender neutrality and trans inclusion by ensuring that it uses gender-neutral language, where it might be offensive, ensuring dress codes aren't specified by gender and ensuring that whenever the JCR holds gender-specific events, anyone who identifies as that gender is welcome.