For Vera Cooper, the time had come to buy a gun.

In her mid-70s at the time and widowed several years earlier, she was already feeling vulnerable, living by herself. Then came the tipping point: The plumbing business that Ms. Cooper owns in the Florida Panhandle had to fire a worker, and he stormed out of the office, threatening vengeance.

At a nearby gun store, she settled on a .22 caliber pistol that “felt good in my hand.” Then came the problem. A question on the firearms transaction form she was required to complete asked whether she was an “unlawful user” of marijuana or any other drug categorized by the federal government as a controlled substance.

Ms. Cooper is registered in Florida’s medical marijuana program and relies on the drug to ease her chronic knee pain and sleeplessness. She answered the query accordingly, and was told that as long as she held a marijuana card, buying a gun was not possible.