Word for a non-politician who commits crimes against humanity

I would use enslaver rather than slave driver, and also exploiter possibly in combination with an adjective like monstrous.

Several good suggestions have been offered in the comments above, including "capitalist thugs" and "soulless profiteers" (Doug Glancy), "oppressor" and "tyrant" (ghostarbeiter) and "despot" or "tyrant" (Jesse M.).

I generally use the term capitalist whore instead of capitalist thug, but, of course, many people will complain that that term is obscene. (Ironically, the people who complain about it the loudest are people who are actually working for the capitalist whores.)

I'm not intimately familiar with the story of the rubber barons, but they might be described as imperialists, especially if they were based in or closely tied to the U.S. or Europe. The term Yankee imperialists is often applied to corrupt entities based in the U.S.

You might also incorporate the term colonial (e.g. "colonial pigs"), especially if Brazil was still a colony when the reign of the rubber barons began. Even if Brazil was already a sovereign state, the rubber barons might be seen as a legacy of colonialism, which exists even today. The term plantation master can have a similar connotation.

Another possibly useful term is monster.