We already have a system in place where we don't have to accept every qualified prospective member. The investigating committee makes a report, and the membership present at the meeting votes on whether to accept the candidate.
Having said that, I think if we have a situation where an auxiliary systematically refuses to accept an entire group of candidates solely on the basis of their gender (like you are suggesting when you say to leave it up to each auxiliary to decide), we may run into a legal issue due to gender discrimination. We don't need that!!
I've completely changed my mind on this issue over the past 2 years, and now I believe this is a concept whose time has come. Why? Ladies Auxiliary membership is dropping every year. (Last year, our net loss was 10,700 members - the year before, we lost 16,400.) Costs are rising every year, and our investments are flat. We need people, and we need money - urgently.
Meanwhile, the men's auxiliary concept does not seem to be thriving in its current state. For example, our men's auxiliary members at my post work their tails off - and the post members crap on them because they somehow perceive they are being upstaged by men who aren't combat vets. Our men's auxiliary actually paid our post's mortgage all summer (for the 3rd year in a row) with no appreciation whatsoever.
The ladies auxiliary organization will be 100 years old next year. If our organization is so fragile that we can't absorb a new group of willing prospective members, then shame on us.