When the police give up their right to guns, and the government can guarantee no criminal will ever have one, I'll give up mine.
Actually I won't, but good luck making my conditions a reality.
I can only speak for the agencies which employed me. To become an armed officer of the law, the applicant is required to pass a written test, pass at least two and most times three oral interviews, take and pass a battery of psychological tests and meet with a psychologist at least two times before offered a conditional offer of employment.
Then a full background investigation will look into the life background of the applicant: Arrest history if any; treatment for Alcohol or other drugs; civil court orders and judgments; found to be a danger to them self or others; Credit history; Residences, reasons for changes of location; education, incl. academic and deportment records; interviews of three persons who provided recommendations and others who might know the applicant (former neighbors, employers, teachers, coaches, etc.).
He/She then must complete POST training in the laws of arrest and firearm training, the latter of which is on going for their entire career. Sign off on a use of force policy and for the first (usually) year continue to be trained by a Field Training Officer (FTO). Not until the probationary employed proves him or her self in the field are they offered permanent employment. At any time before that offer is made, they can be sent home with no right to appeal.
If you Marty wanted to own a gun, and such a background check were required, your written comments on this Message Board would be sufficient and necessary to tell you, Hell No! You would never be allowed the privilege to own, possess or operate a gun of any kind!