Slate's Explainer talks about the expelling players from the Hall of Fame for "character" issues:
The Hall has no mechanism for expelling its members. (Other major Halls of Fame--baseball, basketball, boxing--don't have policies for kicking out players either.) Nor is being good person a requirement for induction in the first place. The institution's bylaws explicitly state that off-field behavior doesn't affect one's eligibility: "The only criteria for election to the Pro Football Hall of Fame are a nominee's achievements and contributions as a player, coach, or contributor in professional football in the United States of America." That, and a player or coach must be retired for at least five years.As a result, most Halls of Fame--even baseball's--include more than a few unsavory characters. Ty Cobb was a well-known racist. Kirby Puckett's former wife accused him of longtime abuse. Dallas Cowboy Bob Hayes dealt coke. O.J. Simpson kept his crown even after he was forced to pay millions in damages in a civil case filed by the family of Nicole Brown Simpson. (In 1995, someone stole the bronze bust of O.J. from the Hall's museum and apparently threw it out a car window on a Cleveland highway.