Hard to compare the PGA Tour to a private club. If I'm not mistaken Michelle Wie played in a couple events quite a few years back. Which seemed to be a mistake in retrospect however, I don't think there was an issue with her competing. Not sure if any men ever played in an LPGA Tour event?
Incidentally, I just received a call from the artist formerly known as Bruce Jenner, she was curious if cross gender members could keep their membership if the sex they currently identify themselves with was different from that which was on their birth certificate?
(sorry couldn't resist, but it's not unthinkable that something of this nature could pop up, although unlikely that it would happen in the UK at least before the US)