This is an issue that absolutely burns my ass. I always answer, "I refuse to answer any questions not directly pertaining to my healthcare." So far, I have gotten no push back. If I ever do, I will explain that first, it is a violation of PERSEC (personal security) to discuss such things with outsiders, and second, they are acting as an agent of the government, and I will not forfeit my 4th and 5th Amendment Rights to them or the government itself. Those questions would only be answered in, and under the advice of, my attorney.
An amicus curiae brief just filed by the Second Amendment Foundation and Citizens Committee for the Right to Keep and Bear Arms shows the real reason that Floridians were outraged when an Ocala, Florida pediatrician in 2010 kicked a young mother and her baby out of his practice for daring to object to his inappropriate questioning about guns.
When the government states, "thou shall not treat patients that refuse our inquisition," I will seek out the black market, cash only doctor. I guess I could always just answer truthfully, "I do not own or possess a single firearm."