Jud, an interesting question. I have been invited to join such a club in the UK and have given it some thought. In the end I concluded that in some situations I have no problem with men only clubs, and in others I am not interested. Let me explain.
I believe I have the right to associate with whomever I wish. And if some of those associations are through a club that will allow only males as members, that is fine.
However, I personally have no interest in associating with members (or belonging to a club) that is male only and flaunts that attitude. Some clubs, primarily in the US it seems to me, are male only and are proud to promote exclusionary membership and guest policies. The culture of the club revels in keeping women out of membership and away from it facilities.
Other male only clubs, primarily in the UK, have a different culture. There women are welcome in the clubhouse and golf course. In fact many of these clubs have associated womens clubs that share the course or have their own course - Royal Aberdeen, Formby and Royal Troon come to mind. In St Andrews, men have several clubs that are male only and there are, I believe, 2 clubs that are women only.
I don't think I would want my primary club to be male only, I enjoy the company of women, especially my wife, on the course and in the clubhouse too much.
I know some feel that all clubs should be open to all, and I respect that view, I just feel differently.
One final point, slightly related. I have never been to a mixed club where associations were not primarily men with men, and women with women. That just seems to be the primary way we humans associate with one another.