Never tell them anything. Ever.
Here's the way to handle this, and I have to tell people over and over to do it this way.
Do not go into " This is none of your damn business, mah constitution !!!"
Don't even say it's none of their business.
Don't ask them why they're asking the question.
Play along, and smile. '
This is your answer.
" Nah, I ain't hunted since I was a kid. I do like to fish though. Man that's peaceful and relaxing. I got this spot over by ( name a spot somewhere near ) , and man they usually bite good there. One day when you're off if you like to fish you outta come out here and fish with me."
You have created a friendly dialogue, you have reached out to the Dr. as a friend, and you have not said anything negative. You've substituted a very common activity that is considered "normal" and non threatening.
If you refuse to answer, guess what, you answered, you've told them by your refusal that the question bothers you because you have guns and don't want them to know. They will mark that as you being a gun owner. They may mark no on the front sheet in front of you, but they will change that once you're gone.
If you get in a huff, angry , or respond like it bothers you, then you have answered yes, and they will note it. They will also note that you may be too unstable to own guns depending on how short your fuse is and how angry you get, multiplied by how far left they are.
So,, in conclusion friends, invite them fishing.