This is completely dependant on the situation.
They have done studies with nurses who are also highly trained, and they found that the more stressful the situation, more urgent, and more strange the more likely that the person is willing to do things they know are wrong when told to do so by an authority figure. In other words, when they had a "doctor" call them in the middle of the night telling them that they needed to give a patient some unkown drug right away, (they told them to give a very large overdose) 9 out of 10 would listen. However, if it was not urgent, or if it was a drug the nurse was familiar with, none of them would do it.
If you had a peaceful march that looks like a parade, it is very unlikely that the soldiers would fire, however if the protest was getting a little out of hand and they started to push on the soldiers the soldiers would be much more likely to obey orders.