Two very important parts of the moral sense are protectiveness towards babies and children, and a sense of disgust and fear of contamination. (There is an actual scientific debate about whether the latter two are separate.) Our protectiveness towards children is very much an evolutionary product of our being social animals. It's triggered by big eyes, big heads, small bodies, etc.. For example, in contrast to us, male lions slaughter the offspring of other male lions. As any biologist will tell you, there's little difference between a 22-week fetus and a newborn anyway; a breathing reflex, perhaps, and a change in blood flow that happens on birth. But, more innately, when we look at a 22-week gestational age human being in a preemie nursery, our brains see it as a baby, and our protective instinct is triggered. Light-hearted chatter about crushing the bodies of late term fetuses disturbs us, and it should. It's completely natural we feel that way. Blather all you want about it not being a baby; your brain knows better.
Now compound this protectiveness with disgust and fear of contamination, which exists, among other things, to protect us from eating bad food. There's a reason why we say 'not while I'm eating lunch' in response to disgusting stories. Watching conversation about dismembering babies, while the speaker is eating lunch, sets off two alarms. If it doesn't disturb you, you're probably a sociopath. And we don't like sociopaths, because we rtightly fear and shun people who don't have instincts that allow them to live peaceably with others.
Interestingly, research -- a lot of it done here are UNL -- shows conservatives tend to react more intensely to disgust (and conversely, disgust tends to make people more conservative). And liberals tend to be more protective, which is why they hate fetal pictures. This tape manages to trigger all of us.
Libertarians and liberals tend to argue we can transcend our innate moral sense, where it doesn't squae with our rationally based ethics. Peter Singer, for example, argues that if newborns and late term fetuses are essentially the same (and they are) we should be able to kill newborns just as we perform late-term abortions. Libertarians sometimes argue our incest taboo (another part of the moral sense, linked to disgust) makes no sense applied to sex between consenting adults who can't conceive deformed children, such as same-sex and infertile siblings. They're pissing into the wind.
Conservatives, on the other hand, argue that the moral sense is incredibly important. We humans are simply not smart enough to do complex ethical calculus on the fly. We need a moral instinct, just as we need an instict that lets us figure out the flight of a baseball, and can't just integrate Newton's equations of motion, as a computer would.
We trifle with this stuff at our peril. There's no evidence our moral sense is a cafeteria from which we can pick and choose.