There are a couple points.
If you are a convicted felon, you normally lose the right to possess a firearm. Similarly, if you have been convicted of a crime of misdemeanor domestic violence, you also lose your right to possess a firearm (lautenberg law).
The Lautenberg law was written without a military/gov. worker exception. It's pretty hard to join the military, if you can never qualify with a firearm because you cannot legally handle one!