As a private citizen, no. As an individual in a position of authority and either on the state payroll, or operating with a license from the state, yes.
You cannot let the government control what someone has to say outside of the typical five understood exclusions (libel/slander, etc.)
Sure you can, when such speech constitutes harassment at the least, and a conspiracy to deprive the American people of their arms at the most.
This weapon is just like mandating that restaurants have to forbid smoking.
No it isn't.
There is no conspiracy of doctors - and 'none of your business' is a legitemate reply AS IS boycotting doctors who do ask that question. That is how CONSERVATIVES get things done.
Yes, there is absolutely a conspiracy to disarm the American people.
"None of your business" is certainly a legitimate reply, but as others have noted, if you so reply, they will check "yes" on the gun ownership box. Also, the doctor could ask the question of others living in your house, such as a child or an elderly parent with diminishing mental facilties; either of which may let the cat out of the bag.
For instance, the next question could be "since there are guns in your house, are they ever left around so a minor can access them?". Granny, not knowing any better or not even understanding the question, may answer "yes". In many states, that is a crime, and a doctor will report you to the stasi.
Boycotting doctors was certainly an option 50 years ago. Today, in our quasi-socialized medical "system", it isn't so easy.
I suppose one could argue for getting the government out of the medical system, but that isn't going to happen realisticly. The next best thing is for state legislatures to actively protect individuals from harassment by doctors.
The state forces me to have a liscence to practice medicine. The state also requires you to have a liscence to drive as they have socialized the road system. Does this mean the state can control what you say while you are driving your car?
Sure you can, when such speech constitutes harassment at the least, and a conspiracy to deprive the American people of their arms at the most.
Harassment is a legally concept that 'are guns in your house' question does not reach. If the doctor actually did something that constituted harassment, there are already legal remedies in place to address it.
And conspiracy? It's a really bad idea, but to suggest this is some back-door gun registration strategy sounds like you should be wearing a tin foil hat. Do you actually have proof of a conspiracy?
I remember a few years ago when my son, who about 12 at the time, had a physical. I had left to use the bathroom and came back just to hear the doctor ask my son about guns in the house. I answereed coming through the door and said I believe and it was none of their business. And if I did I certainly would have a gun safe. The doctor shut up at that point. Later on the doctor asked about bike helmet use and my son answered that he does not except when I tell him to and that he felt that that should not be law but up to the parents decision to wear a helmet. The doctor was a bit surprised but answered that if he saw the head injuries and the medical cost to society. I answered that that was inaccurate as any medical cost that would occur from a head injury would be covered by my insurance and myself and any further care would be my responsiblity. Society does not pay my insurance premium, I do and so does my employer. So that arguement was false. She went on about surely we agreed about seat belt use and I said no I did not agree to have the state make laws about any risk taking. She argued about the terrible injuries that can occur. I said I personally looked at wrecked car as a insurance adjuster and still did not think that that should be a law. I then went on about how based on her logic that the state could regulate any activity we do from skiing , horseback riding climbing since all involve physical risks . Therefore I did not feel that the state had any justification to make laws about helmet use and seatbelts. In fact the state has usurped my authority as a parent. This absolutely stunned the doctor especially when I said I saw wrecked cars and the drivers all the time and still did not agree the state should jump in and regulate. I definiately see the results of car wrecks more than she does as a pedetrician.
My son at that time had not realized how I would argue against an authority figure. It raised my status in his eyes and even heard him talk about that with his friends in the boy scout troop.The boys felt quite free to confide in me after that.