So, I saw a recent poll by concerning Order 66 and whether or not you would follow it.
Unfortunately there were only two options: 'yes' and 'no' when a 'maybe' or 'comment' option would have been an excellent addition and here is the reason why.
It is very hard to ask the average person if they would follow the order to turn on their commanding officer. As a military man I can safely say that I don't know what I would do if I was ordered to detain or execute my commanding officer. In fact I would be highly conflicted as to the correctness of such an order.
The advantage that the clones have (though not universally) is that they obey orders almost unquestioningly. It is drilled into them from birth that they will obey the orders given to them and even when they have misgivings they frequently fallback on their orders because that is where they are most comfortable (again, there are exceptions to this).
That sense of obligation to follow orders is not something that the average person has. We all like to humanize the clone troopers in Star Wars, they're often quite lovable and endearing characters but I think often enough we forget that deep down, despite whatever emotional turmoil they may be harboring within, they are generally going to follow their orders.
What does this mean? Well, quite simply, it means that the average trooper when in receipt of one of the Contingency Orders is simply going to execute that order without question because they have been instructed to do so.
Whereas you or I might stop and think about it, and puzzle over whether or not the order is 'right' or 'wrong' most clone troopers will simply see the order as an order and leave the morality out of it.
Now is this universal? No. As I have said a couple times now, there are exceptions. Not all clone troopers are identical despite the kaminoans best efforts to ensure they are and some are downright divergent. However they are not the norm, the norm is the trooper who simply receives and obeys his orders without question.
That is something that someone even as highly trained as a human soldier can't fully comprehend because even the most highly trained soldier, on some deep level, has the ability to question orders issued regardless of whether or not they follow it because they were not always soldiers. Somewhere inside there is still a civilian, one that may even secretly buck at the authority executed over him.
Most of the rank and file clone troopers don't have this conflict, they simply have the execution of their orders in service of their duty.