I'm all pro-female visibility and such, but I think the search process shouldn't explicitly exclude men. Hosting shouldn't automagically exclude a whole sex.
Specifying a desired sex for applicants is not OK in Washington State. Even in a case where there is a male in an equal position. We have non-discrimination laws here. They are clearly discriminating in favor of females for this post.. There are exceptions to accommodate religious or social requirements relating to contact between people of different sexes but this job wouldn't meet those standards.
@9, I can't find an RCW or otherwise official source describing the exemptions you mention, but "social requirements" seems pretty broad on the face. Why do you think an employer couldn't decide to have both a male and female employee so that any male or female client/customer might feel more comfortable having someone of their own gender available?
I'm out! Next!