just be LDS, but someone who embraces and lives the tenants of the Church. They want someone who's first priorities are to encourage and help the young men serve missions and be active in their Church. They will embrace Church policies for the most part and try to get student athletes to understand and honor them. Those who are not LDS will not have that same ingrained priorities. They can certainly understand it and push for it but it is not the same.
Like it or not, BYU IS a Church institution and if there is reason to "secularize" the athletic programs, BYU will go the way of BYU Idaho and drop it's athletic programs.