To shake a stick at something is not a threatening gesture down south. I guess it could be, but it’s an expression used to demonstrate an excess of something.
“She’s got more boyfriends than you can shake a stick at.”
“We’ve got more tomatoes this year than you can shake a stick at.”
The underlying idea is that shaking your stick wouldn’t do anything to get rid of the excess.
How have you used this phrase? What have you seen so much of that you can’t shake your stick at it?