They're completely unafraid of wriggling out of or defying their orders whenever they don't want to do something. So why is it that they go ahead and do this despite not wanting to? They're personally loyal to each other, but that's all, they don't care at all about any other Shinra or civilian lives. If they really don't want to do it, why did they?
Tseng says it point blank in Chapter 16 (I think?). There's a scene where Reno, Rude and Tseng are sitting in the latter's office. After Reno suggests that he's not happy with the way things went on the plate, Tseng tells him to take a vacation. Rude then points out his concerns with what they did, and Tseng tries to calm his conscience by telling him if they didn't drop the plate, someone else would have been ordered to.
I haven't seen any other evidence in the game yet that they can just willfully disobey orders at will. They're loyal to Shinra, and most of the time, we see Reno/Rude conducting business on behalf of Tseng, who gets his marching orders from the top.
Everyone else within Shinra is written in a more one dimensional way (yes, I know about new recruit gate guard person, that's not enough) .
In the OG? All the soldiers in Midgar were faceless grunts. I don't remember any single soldier having any kind of characterization until you hit Junon, and that was mostly for comic relief.
OTOH, the Remake has the gate guards, the soldier who recognizes Cloud (also the same soldier who recognizes him in the Shinra Building?), the soldier who freaks out and runs away when Cloud throws the sword into the window as they're escaping, and the soldiers arguing about their jobs with Reno in the church while Aerith is stuck. That's not counting the soldiers' terrified reactions to Roche at the upper-plate Shinra base, the information gleaned from the Assess tab, the reference to Kunsel or the unique variants like The Huntsman.
Everyone except the Turks. It comes off like a ham fisted attempt to take responsibility away from the people that actually pulled the trigger.
Ultimately, that was President Shinra's call, and the action stops for several minutes so that he and Barret can argue about the difference between Shinra and Avalanche, and why the former adopts the "end justifies the means" mentality. The Turks turned into comic relief as soon as you stepped outside of Midgar in the OG. When you meet them in the Crystal Cave(?) and Gongaga, Rude mentions having a crush on Tifa, Elena shows up and spoils the group's plans, and Tseng acts exasperated before walking off. This from the same group that tacitly oversaw the operation and displayed no remorse or conflict at doing the job.