I'm not saying it is illogical because it is evil or mental. It is an act of faith or obedience, neither of which is arrived at through a logical thought process.
The religious nut does his duty because he believes he has been instructed to do so, not because he has weighed the pros cons and consequences of the act and believes it is the only logical course of action.
I get your point, its just the wrong word. And however you dress it up it remains an act of faith, however misguided.