Oscelot: Mikoshi processions are very common, although I don't know whether the US shrine does them. They're usually a bit more sedate, though; mikoshi are very, very heavy.

I don't know of any examples where adult women participate in loincloths and happi coats, though. There is a big festival in Kyushu where everyone dresses like that and the children's mikoshi is open to both boys and girls, but even there I think the adult ones are all male.

Sexism, that's what it is.

Actually, it's pretty common to wear shorts under the happi, and women do participate like that.