The last half century or more has had the word "conspiracy" be used almost exclusively for disparaging theories as crackpot or insane. Which has change the colloquial definition away from the actual one.

So for most people the "Jewish elite conspiracy theory" does sound a bit insane, because a "conspiracy theory" label means they are doing absurd, almost comically evil things that would require 200 IQs, literal psychic foresight, and them to be an actual superior race to be capable of.

When the actual one is, as you said, probably pretty mundane but in enough positions of power for a long enough time that its basically still wildly powerful and giving them great ability to do evil. The end result is probably close to the same though.