If the law is changed to no longer allow access to these records [...] what other open records will also be challenged? Probably several, including the sex offender public records.
Yeah, 'cos a person who voluntarily got fingerprinted, filled out a seriously nosy form (it is a felony to give inaccurate info therein) and passed a State Police background check is just like a convicted sex-criminal, hey?
No. Let's review: sex-offenders have committed a crime. Handgun carry-permit holders have not. While there may be some question about the degree of offense and suitability of the punishment for some sex criminals (drunk guy caught tinkling in an alley, etc.), it is in no wise the same sort of thing as the legitimate exercise of a genuine -- if severly circumscribed -- civil right.
How would this play out if you had to get State approval to practice your religion in public? (Let us not ignore the violent potential of religions; in Europe alone, from the Reconquista to the Reformation, the toll is appalling). Would the same writer be fretting about how protecting the privacy of Lutherans, Jews and Unitarians would lead to challenges against a public record of sex offenders?
Your baseless fears do not trump my inalienable rights.
Update: Ever notice how there's a lot of overlap between the crowd who wants carry-permit records open to any mook who can afford the copy fees, the gang that wants "Lost and Stolen" laws that criminalize gun owners who don't report gun-thefts promptly and the ijits who use stolen gun stats as an argument for more gun control? Yeah, that's how it works -- enable the crime, punish the victim, use the crime to argue for tighter control; lather, rinse repeat.