There is now a bill before the House (House Bill 1623) to make this information not so readily accessible to just anyone. From what I have heard on the news, it did pass the House.
Update
On the House floor Friday, members approved HB 1623 by Rep. Randy Stewart, D-Kirby. The bill would make the names and other information of holders of permits to carry concealed handguns exempt from the Arkansas Freedom of Information Act.
Stewart said he filed the bill after a weekly newspaper made a list of the state’s permit holders available to readers.
“You apply for this … permit with a reasonable expectation of privacy. That’s why it’s called a concealed handgun,” Stewart said. The bill passed 98-1.
SOURCE: AR News