I am not so sure. When you start impacting people’s livelihood, careers, and future, the line is not so clear. I think many of the soldiers would follow orders, because of what they face by disobeying the orders—prison,loss of job, etc. It would need to be a flash-mob sort of mentality to occur for many to actually disobey that order. This sort of thing occurs daily in jobs everywhere, an employee has a problem with a supervisor, but push come to shove, it is likely not going to happen that a fellow employee will stand with em because of the potential loss of job and all that goes with it by standing with the employee.
There have been instances wher GIs have stood up against wrong doing regardless of the negative effects. Travis Riots is one example.
I know of entire work sections that have refused to work because of stupid orders. They were threatened with all types of legal actions and they just said “go ahead”.
When stuff gets crazy the GIs will make a stand and careers be damned. It happened before and will happen again.