That group was and still is a code word for "racist", "sexist" White Supremacist-types who you don't want to have dinner with if your anyone of a normal mind.
Here's the details from FireDogLake and BAGNotes:
Michael Shaw at BAGNewsNotes found this 1995 image of Sarah Palin at her Wasilla City Council desk. It appears to be her official portrait, and a mundane one at that.
What's striking, as Michael points out, is the article in front of her: It's a piece about the "Con Con Call" -- one of those hysterical non-issues that conspiracy theorists of the far right in 1995 were shrieking about, involving an attempt by a handful of governors to organize a convention aimed at fighting what they saw as states' subordinate status. (Yes, the shrieking shut it down.)
One of the organizers of that particular torch-bearing mob was the John Birch Society. And sure enough, the article that Palin is proudly displaying in this portrait is a copy of the March 1995 edition of New American, the house organ of the Birch Society.
The article in question was written by Don Fotheringham. (It's no longer in the NA's archives, but you can read the text of it at this site.)
The Birchers are best known for their ardent McCarthyism and their long career in promoting cockamamie conspiracy theories about supposed Communist infiltration of government -- not just in the '50s and '60s, but well into the late '80s, until the fall of the Soviet Union. At that point, they simply picked up the same act and transferred it to promoting similar theories about the "New World Order" under Bill Clinton in the 1990s. (Chip Berlet has one of the best disquisitions on the Birch Society's long career.)