See Urban Meyer...
If Utah wrangles in a well respected non-LDS coach, not only will that help their non-LDS recruiting, but also top LDS talent as well... I don't think most top tier LDS athletes are all that concerned about their coach being LDS... i think they desire BYU for the fellowship they will get with other students and people at the school that share their beliefs.. Regardless of who the coach is, both Utah and BYU will always be LDS rich schools... So if an LDS kid believes he can fellowship with other mormons and have a really good coach, Utah could be positioned better than before