san francisco bay queer contra dance
a little bit folky a little bit flirty a whole lot of fun
other gender-role-free dances

There are several contra dance groups across the U.S. which don't fuss about gender. The umbrella organization Lavender Country and Folk Dancers (LCFD) includes most of them (including Queer Contra Dance) and is also a good source for more information about gender-free dancing.
bay area lgbtq dances
bay area contra dances
additional links