Except at some point, they will either make lying to your doctor a felony (falsifying medical records), or use it to establish a baseline of mental incapacity (i.e., he owns guns but doesn't acknowledge it = denial of reality). Either of which will bar you from gun ownership under the uber-state.
I disagree. Play along and innocently tell them no and there will be no more questions on the issue.
However, if you get defiant, belligerent, and sarcastic, it will be duly noted that you have something to hide.
When the time comes, it’ll be the uncooperatives who get their homes searched.
Lie to them. Lie convincingly as if you agree with them. This is how Jewish sympathizers survived in Nazi occupied territory.