Cesar Chavez speaking to the press in Los Angeles in 1976. David F. Smith/AP Groups with ties to Cesar Chavez, the Hispanic labor and civil-rights icon, are distancing themselves from the leader who died more than 30 years ago, after allegations that he abused women and girls at the height of his prominence in the 1960s and '70s.

A wave of Cesar Chavez events have been canceled at the last minute across California after "profoundly shocking" claims of sexual abuse came to light -- and insiders warn it could just be the tip of the iceberg.