Who cares?

I care. I certainly care about attracting half of humanity to rationality groups more than I'd care about attracting that subset of males that would be significantly distracted in mixed-gender company.

Besides, as a practical matter what I envision is occasional meetings where girls are excluded. I think it would also make sense to have girl-only meetings.

At the start of this discussion you used the term "men-only". But in contrast you're consistently using the term "girl" to refer to a member of the opposite gender.

The corresponding term to "men" and "men-only" is "women" and "women-only". If you'd used "male", the corresponding term would be "female". Only if you had used "boy" or "guy" could the corresponding term be "girl".

Take care of the connotations of your word choices, especially given the content of your suggestions.