My impression was along the same line as yours. I also figured they disappeared when the USSR did. It has to fire up the membership more to warn about the existential threat of an evil empire stretching across 11 times zones than to warn about a tiny island where repairing 60-year-old cars is a specialty.
I did a Google search on "John Birch Society anti-semitic". Lo and behold, the first three items were all letters to the editor to newspapers across the country from "Alex Newman, Coral Gables, Fla".
It explains why someone from FL is interested in an ordinary newspaper well over 1,500 miles from where a letter writer lives who should be buttoning up his overcoat and battening down his hatches. It's going to get a tad windy soon.