I didn't say "Judaism", I said "Jews". (There is a difference). The Rothschilds are a Jewish family. That's the link.
Traditionally, it was fashionable to claim that Jewish financiers ruled the world (see the Protocols of the Learned Elders of Zion) But in today's politically correct times, conspiracy theorists find it safer to claim that "global financiers" rule the world... and then they identify the Rothschild family as one example.
The Money Masters has an entire segment (nearly 6 minutes long) devoted to this aspect of the theory. That segment is entitled The Rise Of The Rothschilds.
Yes, a lot of people went into debt during the Great Depression. Many of them were shareholders and financial giants. Many others were regular people like you and me. And many banks failed as well.
However, notice that the Wikipedia article does not make the claim of the conspiracy theorists; it does not claim that the Great Depression was deliberately engineered by the Federal Reserve.