Why do people still follow the one drop rule if Jim Crow laws ended?

Jim Crow MANDATED discrimination. NOTHING can prevent individuals from being bigots.
That said. the VAST majority of people don't even know what you are referring to as the 'one drop rule'.

"People" in general don't but there are a few whack jobs (usually lacking education or a reasonable IQ) that still do. Otherwise how can they claim to better than anyone?

Who says they do?
And why should any of it matter.