Sadly, many weak people are intimidated by DOCTORS. We need to get the word out that doctors really aren’t God. People need to know they don’t have to answer this question.
Refusal to answer or a defensive answer such as "That's nobody's business" will probably just go down as a Yes. Or perhaps "Yes - combative response". This is time to listen to Nancy Reagan - "Just say no". The first inclination any stranger will have that I own guns is when they see the fire coming out of the barrel.
I suspect that refusal to answer will also go into the data base and be inferred that you have guns and/or are conservative. A better answer is to lie, but many people are going to have an ethical problem with that approach.