One of the reasons that I have never liked the "insanity defense" for murderers is that, to me, everyone who kills is insane.
There are people in this world who have such a hatred for others that they can and do kill. It is happening right now in the Middle East. The "suicide bombers in Iraq" are a case in point. They truly hate those whom they kill and truly believe that they will go to a beautiful "here after" for what they are doing.
One of the things that civilization is supposed to correct is man's cruelty to man or, if you like, "man's inhumanity to man". We are the only species on this planet that kills for sport or revenge or anger.
It doesn't seem implausible to me that a group of men could kill seven Romanovs (including the young women and Alexei). We have all either lived through or studied the Second World War. The holocaust was a greater crime against humanity, but Hitler had no problem finding men to go along with his ideas and expedite them.
In some countries human life is "cheap", by which I mean, the killing of people in those countries does not bother people the way that it bothers us. I believe in Russia in the beginning of the 20th century that those who fought the autocratic system had seen so much violence and killing not only in the Great War but also in the wake of autocratic decisions, that they did not hold the Romanovs' life with any respect at all.
To those guards, it was just another job. They were just "following orders". It may be true that some of the guards did not have any idea what the actual event would be like and the killing did make them sick. But there were those, Yurovsky included, who no longer saw the Romanovs as human beings, but more like trash to be taken out.