You misunderstand, the idea of the “Long March Through the Institutions” is that innocent conservative intellectuals are the victims of a central, coordinated campaign for them to be expelled from academia in order to transform academia into an institution that serves leftwing agendas. It’s an explicit rejection that such a transformation could occur naturally, and can fairly be considered a conspiracy theory by the mainstream specifically because it meets Barkun’s criteria for conspiracy theories:

  - nothing happens by accident
  - nothing is as it seems
  - everything is connected

as well as the lack of a smoking gun.