Living in Washington State, I don't have to worry about the local papers doing any such thing. WA law prohibits the release of names or any other information of CCW permit holders to the general public. Only police departents and the Department of Corrections may view CCW holder information. Also, WA CCW holders are exempt from background checks under the federal Brady Act.
Unfortunately, some people who interpret the First Amendment as a means and a "right" to futher their own political or moral goals are the ones that should also have their private affairs open to scrutiny. Newspaper editors and "journalists" who thumb their noses at the rights of other people simply because they are acting under the freedoms of the First Amendment just don't seem to understand that in some cases the "freedom of the press" can hurt good citizens as well as help.
The best defense agains these type of people is to use their own newspapers to publish a response or rebuttal to their argument. If they truly believe in the First Amendment and freedom of the press, they will have to allow citizens who (just happen to) possess CCW permits to explain to the rest of the communnity why they have the permits and why it makes the community a safer place to be.