The standard story is that the Mafia wouldn't do certain things (such as deal in drugs) until the 60's. That before then they limited themselves to victimless crimes.
If this story is true then the Mafia made money off sodomy and pedophilia. However bad dealing drugs is, those are worse.
So this story is total bunkum or the Mafia has been rotten to the core from a lot longer than we were originally led to believe.
The gay/crossdressing rumors about Hoover were probably created by his enemies.....he held so much power, even more than many Presidents that they had to knock him down in some way. He had secret files on everyone from hollywood to politicians they acted like they had secrets on him
The mob's control of the gay bars in New York is well known. It was their payments to the cops that kept them from getting raided. That they'd have been involved in male prostitution as well as female prostitution doesn't seem particularly shocking.
As far as the narcotics business, you've been watching too much TV. The mob was involved in the heroin trade back in the 1920s. Lucky Luciano had major control over the operation, and established the smuggling routes (often through Montreal) early on.
A few of the familiies tried to keep their people away from it, but it wasn't out of moral concern--it was out of worry about the attention it would draw from law enforcement.