In 1978, there was a mass murder/suicide by members of a cult called the People’s Temple. It was led by a man named Jim Jones. On orders from Jones, over 900 people perished, either by being shot or by drinking a cyanide-laced drink. Although the actual drink was called Flavor Aid, Kool-Aid is the more popular drink of that kind and is usually the one people use when discussing cults.
So when someone on an A/Q site refers to someone “drinking the Kool-Aid,” they mean someone who has completely bought into the cult-like tactics.