Just throwing this distaff perspective into the mix:
I bristle at the mere use of "Mrs."
My OC BBQ wedding reception was held at a different male members-only gun club.
Spent a good deal of time thinking about this when I first ran into a male-only gun club. Considered it in light of things like Second Amendment Sisters, Women on Target, etc. Decided some people feel a need for these segregated environments. Their call within the private sphere. I look forward to the day when it is no longer necessary. I doubt human nature will change such that that day arrives.
just to clarify my tongue-in-cheek, bellow-the-belt quip, I too support the right of free association.
However in the context of the OP asking for the public's support for a club that excludes 50% of the population, it just seems a little too ballsy.