In Kansas*, a religious high school refused to allow a female referee to officiate at their game, because they did not believe that women should ever have authority over men.
To the credit of then Kansas State High School Activities Association, they are in the process of considering banning St. Mary’s Academy from any sporting events with their members schools if this is actually their policy.
They should do so, and they so should do so for non sports activities too. Whether that be beauty contests, band competitions, car washes, or educational conferences.
These people are the real American Taliban, and any accomodation will encourage more extreme demands.
*You know, Kansas would be the last place that I would expect this. So say we all, by the might of the Flying Spaghetti Monster.