This idea is new to me. I have never heard about the theory that hotel keys had personal info on them.
But after thinking about it ( for a few seconds), I realize that I have had keys made/replaced/changed
/moved rooms/duplicated etc and after watching how they do it, with no communication with a computer system and
with 30 years in the communication/computer business
can't imagine why anyone would believe in this conspiracy theory.
They certainly have better ways to get you; so if you like
to shred cards go for it. It's not a major expense to hotels.
I simply forget to return them and them just toss them.