In a word, repugnance:
“As pain is to the body so repugnance is to the soul … So too with anger and compassion. Repugnance is some kind of wake-up call that there is something untoward going on and attention must be paid. These passions are not simply irrational. They contain within them the germ of insight. You cannot give proper verbal account of the horror of evil, yet a culture that couldn’t be absolutely horrified by such things is dead.” — Leon Kass, quoted here.
Letting 21st century barbarism grind the corners off one’s conscience is not the way to respond. There are things men can’t get used to and still be men.