Give me a break about this whole church and state thing. That is bull crap. I am so sick of hearing that. Go to Rome and see who influences the government. Go to any of those Bible bashing towns in the South and see what group influences the local government. Its nothing unique to Utah. Deal with it.
About the flag at half staff, I agree with you, but hardly any of the flag edict is followed these days. I just find it annoying that nothing much was said when the flags were at half staff after the VT shootings or 9/11 (No government officials were killed in those events to my knowledge),but when a LDS Prophet dies people care... Hypocritical don't you think.
Technically the separation of church and state only means that the state may not designate an official state religion (such as Italy and Catholicism). But obviously if the majority of the population of a region are of a certain religion, it is impossible to not feel its influence on politics.
The reason people are upset this time around is that it was a religious figure that has merited it. Thats a touchy subject for many people. The Virginia Tech shootings were tragic, but I agree did not merit the flag being lowered to half mast either. September 11th on the other hand did. 3,000 people dying, hundreds of public servants (Police, Firefighters). This is what is considered a national tragedy, and as such merits the flag being lowered to half mast.
All this being said, like the constitution, this is all malleable. How we treat the flag is dependent on the times and situations. Nothing is set in stone. If the governor feels that lowering the flag, then that is his prerogative being the states chief executive.