I don't want the AMA sticking its nose in where doesn't belong either.
The judges should also be big boys and admit this has nothing to do with gun safety. It tells me a lot about their political leanings.
You could argue that it does have something to do with gun safety (the question itself, not who is asking it or why), but it has NOTHING to do with medicine. If they were asking:
"Do you have guns in the house?"
"Yes."
"Do you wear hearing and eye protection when you shoot them?"
That would be a sound medical reason for asking. When they are asking about storage, they're getting into politics. Asking personal questions about drug use, state of mind, sexual lifestyle/activity, etc. is all intensely personal, but it all has direct medical relevance*.
It's not even so much government sticking its nose into things, it's the AMA twisting medicine into politics.
*Certainly these could be twisted into political oriented questions as well, or at least the data collected could be used politically. My doctor only asks those kinds of questions verbally, and I've never seen her write them down. I've always assumed they were in preparation for annual blood and other testing and for health triggers. etc. She has never asked me about guns.