The main evidence it has supporting it is the a "post hoc, ergo propter hoc" claim (there was a bank crisis before the great depression). But this ignores a huge number of other factors which also contributed to the GD - massive ecological disaster, huge drops in trade caused by Smoot-Hawley et al, new anti-competitive laws and onerous regulations, new technology making millions of workers obsolete.
The claim that a banking crisis caused the GD is popular mainly because banks are easy to model. It's kind of the economic equivalent of looking for your keys near the streetlamp rather than in the dark alley where you lost them.