OK, I'll try this one again. Disregarding the oddness of interpreting 'share' as 'share with some, but not all', let's suppose you're right and the Court didn't mean 'all members share'.
Drag your thoughts away from men who say they're women for a minute. Think about another, far more common protected characteristic: 'race'.
Some female people really, really like black men. This liking cuts across all colours of women. They start a club to which only black men are invited.
They claim an EA exemption on the grounds of sex (the club's designed for women who like black men) and race (only black men).
Two questions:
1] Is this racist?
2] How may the club legally discriminate against white men, who - despite being great dancers, loving reggae and wearing street fashion - have no appeal to the women and piss off the black men?