Most every gun law carves an exemption for ON-DUTY police and military to carry weapons in an official capacity, except the Lautenberg Amendment. Here is a good discussion of how it affects the Army. The basics are true for the police.
Lautenberg Amendment and the US ArmyNeedless to say a misdemeanor conviction is a career stopper. The irony is that while the Government Exception still allows persons convicted of any type of
felony, including domestic violence, it no longer applies to persons convicted of domestic violence misdemeanors.
What is also true is the the filing of an protective order is also disqualifying. In many cases it is very easy for a vindictive spouse to request a restraining order for no reason other than spite. The level of proof can be non-existent in some courts. Some judges issue such orders "pro-forma" in any divorce proceeding. No one is arguing that wife-beaters should have guns, but given the far reaching ramifications that an accusation of domestic abuse carries courts should see that they are founded. Additonally, courts have neglected to vacate such orders after the proceedings in which they were applicable have passed.
One other attribute of the Lautenberg Amendment that is that it applied retroactively, regardless of circumstances. An innocent person who may have plead guilty to a "domestic disturbance" charge and paid a fine to avoid a costlier court fight 40 years ago has no recourse and is penalized along with the truly guilty. Regardless, the law is unlikely to be changed as any attempt will result in claims the people want to arm domestic abusers.