I'm really curious if anyone has an answer as to why there seemed to be so many large cults between 1960s and the 1980s.
Is it media sensationalizing a more common event or were there factually more large-congregation cults in those years than in the past and in more recent decades? When I think of cults I think of violent/suicidal cults like the Manson Family, Jonestown, Waco Branch Davidians, Heaven's Gate, (Scientology?) but also some of the more "benign" cults like alien worshippers the Raelians, Christian cults like the Moonies.
Almost all of these movements began, reached their peak, and petered out between 1960 and 1980, I know of them survive to contemporary times, but if I'm not mistaken those are the outliers. Are there any ideas as to why this is so, or is my perspective a little skewed?
Not a historian, and let the downvotes commence (and I gladly defer to real historians), but I felt like examining the assumptions of the question. Let's look at your examples:
Just looking at these, while two did peak during 1960-1980, it seems like that's not the norm. I'm also not saying that these are the only examples that should be considered; I couldn't tell you what 1920s or 1930s cults aren't on this list.
Were there so many cults between the 1960s and the 1980s?