Very few states, and only anti-gun ones like New York---in fact, the only one I know off the top of my head---make the lists public. And I think New York goes further with handgun possession permits, which few states require.
Although that was useful for me to personally count the total number of NYC possession licenses, less than 60K each for long and handguns. A real outlier for the US, heck, it was noted as the Soviet Union fell that they trusted the residents of the capitol of Soviet Georgia more prior to instigating a seizure of them, then again, I've read estimates that the real number is more like 2-3 million for the 8 million total in the city.
Most of the stuff is overblown.
I've worked in public and private sector jobs where my or my family's political affiliation, public displays of support (ie. campaign contributions), current and past salary history and other info were all potentially career impacting, and all trivially available to the public. The reality is, that stuff didn't matter too much at all.
New York's handgun laws are both insane. That's a separate issue.
And you have no sympathy for those for whom it's not overblown? "If it saves just one career...."
It's NYC's gun laws that are particularly insane, and ought to go down to a McDonald based challenge, but the Federal Courts, even before Scalia died, stopped enforcing such except for stun guns, even backtracked on Heller with SF's lock up your safety law.
To be honest, I don't really care about concealed carry. I personally think that it's a dumb thing to do, but don't have an issue with anyone else doing it.
But if licensing is required, you shouldn't have any special privacy right. If my dog license is available to whenever asks via FOIA, so should your carry permit.