Hunt, I wasn’t addressing you when I emphasized that Duke is a private university. It’s my response to reading so many other comments (including those on other websites) about how Duke “has to” do X or Y.
A thought about classroom seating and single-gender swimming accommodations: I would deny those, on the basis that the university should not have to accommodate religious beliefs that insist on gender segregation (or the demand not to sit next to a woman) in public places any more than it would have to accommodate beliefs that insist on racial segregation (or the right not to sit next to a [name your race] person) in public places.