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.

Serious answer from someone who's in the NYC group:

in practice, people do care. Both guys and girls are more likely to attend an event with a less skewed gender balance. Gender balance helps attendance at events where there's socializing.

I don't know what kinds of topics you're imagining, but usually we don't focus on topics that need to be single-gender. Our topics are things like clustering algorithms and prediction markets and TED talks. Nothing you really need to shoo the girls or boys out of the room for.

Not that I wouldn't mind a Rationalist Hen Party sometime.

If there comes a time when there are enough rationalists who want to go to rationalist meetups that there can simultaniously be all male, all female and mixed sex groups then that would work and even have some benefits for some members of either sex who could plausibly be slightly more comfortable. I don't care if you also include a group for otherkin.