in my experience going back to at least 1995 and probably before that as well. There have always been LDS O-6s willing to volunteer for the assignment and sign the honor code. It has nothing to do with "government officials" signing a religious document. The military/DoD beef is with BYU's LGBT stance, not with religion per se. I mean, jeez...I have to listen to chaplains say prayer before commander's calls and changes of command for crying out loud.
This is a calculated move by the Dept of the AF to move BYU ROTC to a secular school, probably because BYU has run afoul of the LGBT agenda at large. It's how the AF thanks BYU for 66 years of pushing out quality AF officers.