You don't know of any tournaments that ban female entrants??
What about, sports tournaments? Not just the muscle bound sports but games like Tennis, Golf, etc. There are invariably men's & women's sections and that's that. True, Tennis does have a 'mixed doubles' category, but that's such a tiny component of such events.
We're not likely to ever see men playing women one on one in tennis or golf tournaments.
Has there ever been a legal challenge to the practice of sexual discrimination in chess tournaments? Aside from the title itself, "Women's" grandmaster, "Women's" IM etc. what is the legal basis for barring males from these competitions? There are no tournaments open only to members of a particular religion or race. No official titles like "Protestant Grandmaster" or "Hispanic International Master". I believe such classifications would be "politically incorrect", and would invite litigation. Ultimately, I think they would be disallowed. The situation is similar to the case of Dolly Parton's theme park, Dollywood, where they used to charge no admission to handicapped attendees. A lawsuit claiming "unequal treatment" was brought against them, and they had to end the practice. Kind of sad, though: "Hey you in the wheelchair, fork over the money!" But the same principal seems to apply to chess competition. What is the legal justification for barring a player based on their sex? I don't know of any tournaments that ban female entrants. "Wanna' play Anand, lady? Go right ahead!" So why the one-way exclusion? I am reminded of that scene in "Under Siege" where Steven Seagal (not my favorite "actor") says to Erika Eleniak (what happened to her?) "I thought you were a feminist?" And she says "I am, when it works in my favor!"