There's a lovely golf course near my home, it's one of the better courses around, challenging without making you wish for the skills of Tiger Woods. However, the clubhouse bars women from being allowed in the bar. Why is it that I am allowed to play golf there, which costs me money, but I am not allowed to enter the bar area. I don't play at a cheaper rate then the men do, it is solely my gender that keeps me out. I won't play at that course anymore.
The University Club in NYC at one point had a no women in the lounge area rule. As a female, I paid the same membership dues as the men did, but I wasn't allowed the same rights as the men were, and it wasn't l ike the men were running around nekkid. My membership was cancelled pretty quickly and i haven't looked at it since.
There are very few places where men are not allowed to go (and I'm not talking women's dressing rooms, or restrooms) There are very few women only places. There are still a few single sex colleges, and are slowly becoming co-ed, for financial reasons, I think it was Mills College in California, that accepted a male because he took them to court... but otherwise there are very few men who would fight to do something that is a women's only domain.
When Anika Sorenstan (or whatever her name was) tried to play on the Men's PGA tour, she did quite well, but didn't makethe cut, I heard a lot of guys saying well, you don't see men fussing to play on the LPGA tours -- how many men would hold their heads high and say that ooooh I went all the way to the supreme court to play with the girls...

Doubt it would happen, why? Because the perception is to play with the boys is a step up... it's making the girls more competive.. .but for a boy to willingly play with the girls -- well there's something wrong with him.. that he's not trying very hard...