Emile Griffith didn't agree with being labeled, and therefore never accepted that he was gay. That means that the first openly, self-confirmed gay man to out himself while still actively boxing is Puerto Rico's Orlando Cruz. The former World Lightweight Champion came out in 2012 and continues boxing to this day, although at 37 he's approaching the end of his career.
Cruz was defiant in the statement he made when he come out; he said 'I have and always will be a proud Puerto Rican. I have always been and always will be a proud gay man'. If coming out had an effect on him, he didn't show it; he won his next match in October 2012 by unanimous decision. When the National Gay and Lesbian Sports Hall of Fame opened in 2013, Cruz was inducted as one of the inaugural members.