I believe many authoritarian rulers encourage, or at least overlook, barbarous behavior among their subjects because it lends a certain legitimacy to their own barbarous rule. If a farmer is allowed to behead his wife for adultery, it makes the ruler's beheading of the farmer for some minor crime seem a reasonable punishment.

Within that context, religion has nothing to do with the barbarous practices. Religion may be used as an excuse for them, but the real reason they're allowed is that it makes it easier for the ruler to maintain his power base.

Of course, it's possible for an authoritarian ruler to behave in a thoroughly draconian fashion himself while not condoning similar practices among his subjects, but doing so requires more stringent enforcement which equals more delegation of power and a greater likelihood of some sort of palace revolt.