Devils advocate: Do you really think that the visit with your pediatrician is about YOU. No that's why you took your kid to a pediatrician. Stop being so paranoid, they are trying to assess your child's health and potential risks to their health...not trying to make you feel bad about your parenting style.
Standard of care in most states mandates this interview to screen for high risk behavior kids may not want to tell their parents (drug use, suicidal thoughts, depression, sexual behavior...etc.). The pediatrician should not be filling their head with propaganda, only assessing for things your kids may not want to tell YOU for various reasons (think about your childhood...), and they can offer them further support if needed. Fact is you can sue them if they conduct this interview with your child and you can sew them if they don't...as an MD they're screwed either and any which way.
The peditrician can only legally report the presence of physical or psychologic abuse, or potential thereof, and the presence of STD's. The rest is privileged private info and you can sue them if it comes up anywhere outside of the doctor-patient relationship. They don't care how many times the child has seen you screwing from the chandelier or how much you drink, honestly (if you feel guilty about it then no more upside-down drunken orgys in front of the kids)...they are humans as well with the same habits we all have. If they get preachy it's because they think their style may be better...consider it as a suggestion and move on with your life. If they preach about guns in the house realize that is like you telling your surgeon how to fix a hernia...unless they're gun owners themselves realize their insight is limited and move on. Believe me they are not rich or making a ton of money (they start at 50-60K/year these days in most states thanks to insurance co's, the legal suystem, and parasitic business folk).
Doctors are regulated a lot more than you think...there is no more free thought allowed by MD's in medicine anymore as there are as many regulating bodies in medicine as there are hospitals...the MA gun laws and regs pale in comparison to those in medicine.
Just playing devils advocate here...MD's by nature oppose guns, but only an enlightened few understand what responsible gun ownership entails and means and are shunned by their own profession because they are to "do no harm" [to others] as rule numero uno...the rest get their opinion from the mass media and the dead gang-bangers they see in the ER's during medical training. They can not affect your ability to own guns from these interviews unless you are abusing your kids with them or are obviously putting them in danger (like pointing the gun at them)...but the interview for you as a parent is potentially more helpful than harmful, and in most cases really does nothing for anyone involved.