I don't believe that Sunday play is even close to an issue. Consider this. Almost every other sport at most universities is paid for by football, and not every Olympic sport is played on Sunday. As to a championship, even there the conference could change the day and it wouldn't be that significant or affect that many people.

Football, and some men's basketball brings the money in to the university for sports, but even there, many university's sports have to be subsidized by student fees. The Big12 is not going to keep a profitable university that meets all of its other criteria out of the conference because of Olympic sports.