Pete Rose belongs in the Hall of Fame 'cause he's one of the greatest baseball players ever, and Cooperstown ain't the morality police ... so says Rudy Giuliani.
TMZ Sports talked to the former NYC mayor (and Donald Trump's attorney) in the city on Sunday ... and asked him about the president's Tweet imploring baseball to put Rose in the HOF.
Giuliani doubled down on Trump's message ... saying "Charlie Hustle" has more than paid the price for betting on baseball -- a cardinal sin in MLB -- over 30 years ago.