I am more center than right on guns, but this decades-old argument always struck me as silly, for two reasons:
A high proportion of the volunteer military comes from the gun-loving community, including many conservative rural communities. They are not going to start shooting at their own, the same people that they believe are the "real America."
The myth that the "gun-totin' rednecks" think that they are going to take on the US Army is exactly that, a myth. In the case of serious and violent civil unrest, it is more likely that armed vigilantes would be going after progressive civilians than soldiers. That is something to be feared.