From a quick, non-systematic look, I'd say River Falls tends to follow the traditional gender roles:

There's a core element not mentioned so far that organizers aren't under full control of these things. People tend to go to groups that already match a demographic they are looking for, which causes groups to naturally organize around any demographic where people care about what the other people at an event are going to be like. People will even move to find their people, and the whole idea of "my people" is inherently anti-diversity. When people move, the population where they leave and also where they go are less diverse than before, and in opposite directions. So then what do you do as an organizer in either of those locales? It wouldn't always be the best move for either region to try and recreate what the other one has, because they're serving different populations.

Many Atlantans will remember Roxx Tavern, which became the gay bar/restaurant for people a notch younger than the clientele at the Colonnade. I don't know about the Colonnade, but I spoke with both the owner and the floor manager at Roxx, and they never did anything explicit to attract the crowd they did, especially compared to say My Sister's Room. The owner was even in disbelief for many years and had to really stop, eventually, and go what is in front of me when I look at this room of people, versus what I expected to see when I started this restaurant. I think it's hard to explain the demographic at these restaurants unless you factor in that people form groups together whenever there's any level of comfort you'd expect to talk to someone in that group versus another. When you do factor that in, you end up not needing any other explanation, so this network effect is a powerful explainer.

Inclusivity is extremely important, both for recruitment and just to not hurt people. Because of assortative behavior, though, it seems like there are big limits on how much you can really move the demographic of a group. The most promising options are to not be terrible--e.g. the comments about weeding out the creepers. Beyond that, an inclusive dance won't necessarily be diverse. I prefer dances with gender-role flexibility, but that River Falls dance is bangin'.

As a separate effect, there's a tipping point within an individual event about whether people, especially male-presenting folks, will swap roles very much. There's a lot of friction around bucking any existing gender trend for a dance, and contra dance by its nature is even a little bit worse, because of the way you encounter new couples all up and down a line once a minute, versus a couples dance or a line dance. I guess.... if an organizer or caller wanted to counteract that effect, you'd want to look for some kind of gentle on-ramp for guys to be comfortably swinging a male neighbor,  or an older person to swing a younger neighbor. There are many swings other than the conventional closed one, and even aside from gender and age issues, the closed-position swing is already an uncomfortable hurdle for new attendees who haven't danced before.

Lex Spoon