Because the Birch Society was anti-government - at least anti-what the government was becoming. Remember: “The best place to meet an FBI agent is at a militia meeting.”
I received regular mailings from the JBS when I was stationed in Texas in the early 80s and I used to think it was nonsense. Now I look back on what the JBS was warning and almost all of it has come to fruition.
Militias make more sense to infiltrate because the have guns and can talk violence, but the JBS is peaceful and political. Nobody was ever killed by the JBS.