I'm not sure thieves would specifically target a home where the owner is clearly known to be able to defend such a theft with swift, lethal force.
https://www.youtube.com/watch?v=zQNmj2gSq6A
Response time for the police is usually on the order of tens of minutes. A friend lives in the country and called about a suspicious person and had a deputy show up 3.5 hours later. Thieves know this and will be in and out pretty quickly. They know where to look - under the mattress. In the refrigerator/freezer. In the nightstand. On the top shelf of the closet.
Is this different from a thief "casing" your house to determine if you've purchased big ticket items? If their access to the information is logged (which I know isn't always going to be valid) and you're notified that a civilian accessed your gun inventory record, is that more or less problematic than someone who just watches your house every weekend for a few weeks after, say, Christmas, to see what large packaging you throw out without breaking down?
I'm reconsidering my opinion on public access, for certain, and I'm sincerely trying to be as informed on the caveats as best I can.
This sort of database would not be opt-out.