I don't suggest lying about anything that might actually affect your diagnosis or care. In fact, one item often forgotten that can be important if you are facing an unexplained illness is what foreign travel you've done in the last couple of years, or ever, depending on the symptoms. As one example, I believe US blood banks still impose a lifetime ban on donations from anyone who has lived in the UK for more than some number of months due to the increased risk (still small total risk, but statistically significant increased risk) of contracting mad cow disease.
Do bear in mind the evolving and complicated relationship that exists between doctors/nurses and patients. The days of having strict doctor-patient confidentiality and the doctor working strictly for the patient are coming to an end. And this is when you, the adult are the patient. Things get very sticky when the patient is your minor child.
In (many) States health care providers are legally required to report to authorities any suspicion of child abuse or neglect, including medical neglect. The latter can include not following doctors' medical recommendations for treatment as happened some 13 years ago in Utah
with a then 12 year old boy named Parker Jensen. (Your favorite internet search engine will turn up several news stories in addition to the one I linked to.)
While a mostly healthy adult can probably just avoid having a relationship with a doctor if he chooses, parents probably need to have a decent working relationship with a pediatrician. Kids get sick and the ER is really expensive. Kids will need a physical for many school or other activities. Most schools (public and private) require vaccinations. A good working relationship with the pediatrician can make it very easy to get what some might consider to be a less risky schedule than the standard. And if a kid ever does end up in an ER with an innocent injury that could also have been caused by abuse or any form of neglect is ever accused (ie an uptight neighbor seeing a free-range parenting style next door), a good relationship with a pediatrician can provide useful evidence in your favor.
In my opinion, doctors should no more be asking about firearms in homes than they would ask about a family's religious affiliation or devotion. I can imagine rare cases where it might make sense to ask such questions, but that information should not be sought routinely.
That said, I'm way less interested in "educating" or converting my child's pediatrician or other doctor to my view on guns than I am in making sure my child receives the care he needs when he needs it, while also working to protect my child, my family's privacy, and my parental rights from the risk of overly-intrusive government power.
Charles