I've become friends with women in a purely plutonic way
Are you in the atom bomb building business? (sorry, Kalen, couldn't resist...)
I like Kalen's thought that it is fine to seek out people like you, but that drawing that line at gender is a bit too simplistic. There certainly are women (albeit a small fraction) who would fit in well in the setting of many currently all-male clubs. The problem is that those members lump women into the "other" group to make things simpler, as perhaps only 1-2% of women would be good candidates.
Personally, I rarely if ever feel the need to be in an all-male setting, as my demeanor and opinions are the same no matter who accompanies me. However, I know that others are different and act quite differently around their buddies than they do at home (I am not judging here). For this reason, I understand the reasons behind all-male clubs, although ideally gender should not be absolutely what defines like-minded people.
I do think female and male visitors should have the same rights at clubs (besides bathrooms and lockers, of course). What would people think if black people were barred from the restaurant? Or if you needed to have a certain yearly salary to be allowed?