This is a bad idea. Your personal views - religious, political, whatever - should have nothing to do with your job as long as you don't bring them to work. If it is acceptable to demote or fire someone because of their political views or activity outside of work, we are opening a huge can of worms. I hope everyone can understand this.
In general I agree with your theory. But I think it's different when you want to be the figurehead and ultimate authority over thousands of people. Especially you've helped to strip civil rights from some of those people.