I agree with you. Leave free speech alone.
But you are nuts if you can not admit that this gun thing with docs occured during the Clinton Administration when they were screeching that guns were dangerous to children and that parents who had guns were irresponsible.
They started then telling med students and family docs to quiz parents about guns. It is a form of harassment since these docs are really not experts on gun safety and gun ownership is none of their business. The whole issue came out of a left wing political effort to ban guns through fear. Docs cooperated and lent their authority to a left wing anti-gun hysteria.
They should not be surprised when they find themselves being targeted in the culture war. Doctors should have the brains to stay out of the culture war and not be used as the attack dog of society going after political and social enemies.
Perhaps you are right that there is some political movement behind the questions, but that is also not something that can be legally outlawed. And if you really think it constitutes harassment, then litigate it. Or just get in your Doctors face about it if he brings it up or fire the doctor and start a protest in your community on the issue, etc., etc.