Nostradamus?
https://en.wikipedia.org/wiki/Nostradamus_in_popular_culture...
* At the time your wonky conspiracy brained coworker would be sitting down saying "Nostradamus said xyz, pretty weird man!". That was about it, these were just descriptive "isn't it crazy that..." conspiracies. More current ones have deeper implications to their believers, and tend to contain a prescriptive aspect as well.
If you want to point to the marked rise of conspiracy theorists then you have to at least stretch back to the Kennedy assassination. This is easily the most widespread, actually believed theory, and its impact on people at the time was monumental.
The moon landing theories are obviously prevalent, though likely with fewer true believers and less implications on them.
Even in the 90s this was a rampant thing. Columbine shootings. Cobain's suicide. AIDS.
I would posit that conspiracy theories are a byproduct of mass media. However, you could easily stretch it back further and draw parallels to witch hunts as being attributable to earlier conspiracy theories on a smaller scale.