I think you mistake "conservative" for "religious zealot". The two have nothing to do with each other.
I don’t believe Cheney is religious in any meaningful way. You evidently see religious faith as something entirely private — fine, as long as it’s kept to oneself and off the streets lest it frighten the horses. Such beliefs are more a matter of sentimentality than faith, and are entirely alien to conservatism.
You think a living faith is something for the silly and the weak? You put your trust in power and the force of will? Bah. The enemy will have you for breakfast and s*** you out before lunch.